diff --git a/doc/graphs/von_mises/von_mises_ulps_cdf_4d.svg b/doc/graphs/von_mises/von_mises_ulps_cdf_4d.svg
new file mode 100644
index 0000000000..4b708fc043
--- /dev/null
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diff --git a/include/boost/math/distributions/detail/common_error_handling.hpp b/include/boost/math/distributions/detail/common_error_handling.hpp
index 486fb0b5c8..8d866d50d5 100644
--- a/include/boost/math/distributions/detail/common_error_handling.hpp
+++ b/include/boost/math/distributions/detail/common_error_handling.hpp
@@ -11,6 +11,7 @@
 
 #include <boost/math/policies/error_handling.hpp>
 #include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/math/constants/constants.hpp>
 // using boost::math::isfinite;
 // using boost::math::isnan;
 
@@ -96,6 +97,25 @@ inline bool check_location(
    return true;
 }
 
+template <class RealType, class Policy>
+inline bool check_angle(
+      const char* function,
+      RealType angle,
+      RealType* result,
+      const Policy& pol)
+{
+   if(!(boost::math::isfinite)(angle)
+       || angle < -boost::math::constants::pi<RealType>() 
+       || angle > +boost::math::constants::pi<RealType>())
+   {
+      *result = policies::raise_domain_error<RealType>(
+         function,
+         "Angle parameter is %1%, but must be between -pi and +pi!", angle, pol);
+      return false;
+   }
+   return true;
+}
+
 template <class RealType, class Policy>
 inline bool check_x(
       const char* function,
diff --git a/include/boost/math/distributions/fwd.hpp b/include/boost/math/distributions/fwd.hpp
index 5b212c8ec6..1d88b347ea 100644
--- a/include/boost/math/distributions/fwd.hpp
+++ b/include/boost/math/distributions/fwd.hpp
@@ -111,6 +111,9 @@ class triangular_distribution;
 template <class RealType, class Policy>
 class uniform_distribution;
 
+template <class RealType, class Policy>
+class von_mises_distribution;
+
 template <class RealType, class Policy>
 class weibull_distribution;
 
@@ -148,6 +151,7 @@ class weibull_distribution;
    typedef boost::math::students_t_distribution<Type, Policy> students_t;\
    typedef boost::math::triangular_distribution<Type, Policy> triangular;\
    typedef boost::math::uniform_distribution<Type, Policy> uniform;\
+   typedef boost::math::von_mises_distribution<Type, Policy> von_mises;\
    typedef boost::math::weibull_distribution<Type, Policy> weibull;
 
 #endif // BOOST_MATH_DISTRIBUTIONS_FWD_HPP
diff --git a/include/boost/math/distributions/von_mises.hpp b/include/boost/math/distributions/von_mises.hpp
new file mode 100644
index 0000000000..00c928543f
--- /dev/null
+++ b/include/boost/math/distributions/von_mises.hpp
@@ -0,0 +1,796 @@
+//  Copyright John Maddock 2006, 2007.
+//  Copyright Paul A. Bristow 2006, 2007.
+//  Copyright Philipp C. J. Münster, 2020.
+
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_DISTRIBUTIONS_VON_MISES_HPP
+#define BOOST_MATH_DISTRIBUTIONS_VON_MISES_HPP
+
+// https://en.wikipedia.org/wiki/Von_Mises_distribution
+// From MathWorld--A Wolfram Web Resource.
+// http://mathworld.wolfram.com/VonMisesDistribution.html
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/distributions/complement.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/math/special_functions/bessel.hpp>  // for besseli0 and besseli1
+#include <boost/math/special_functions/erf.hpp>     // for erf
+#include <boost/math/tools/roots.hpp>
+
+#include <utility>
+
+namespace boost{ namespace math{
+
+template <class RealType = double, class Policy = policies::policy<> >
+class von_mises_distribution
+{
+public:
+  typedef RealType value_type;
+  typedef Policy policy_type;
+
+  von_mises_distribution(RealType l_mean = 0, RealType concentration = 1)
+    : m_mean(l_mean), m_concentration(concentration)
+  { // Default is a 'standard' von Mises distribution vM01.
+    static const char* function = "boost::math::von_mises_distribution<%1%>::von_mises_distribution";
+
+    RealType result;
+    detail::check_positive_x(function, concentration, &result, Policy());
+    detail::check_angle(function, l_mean, &result, Policy());
+  }
+
+  RealType mean() const
+  { // alias for location.
+    return m_mean;
+  }
+
+  RealType concentration() const
+  { // alias for scale.
+    return m_concentration;
+  }
+
+  // Synonyms, provided to allow generic use of find_location and find_scale.
+  RealType location() const
+  { // location.
+    return m_mean;
+  }
+  RealType scale() const
+  { // scale.
+    return m_concentration;
+  }
+
+private:
+  //
+  // Data members:
+  //
+  RealType m_mean;             // distribution mean or location.
+  RealType m_concentration;    // distribution standard deviation or scale.
+}; // class von_mises_distribution
+
+typedef von_mises_distribution<double> von_mises;
+
+#ifdef BOOST_MSVC
+#pragma warning(push)
+#pragma warning(disable:4127)
+#endif
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> range(const von_mises_distribution<RealType, Policy>& /*dist*/)
+{ // Range of permissible values for random variable x.
+  if (std::numeric_limits<RealType>::has_infinity)
+  {
+    return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(),
+                                         +std::numeric_limits<RealType>::infinity()); // - to + infinity.
+  }
+  else
+  { // Can only use max_value.
+    using boost::math::tools::max_value;
+    return std::pair<RealType, RealType>(-max_value<RealType>(),
+                                         +max_value<RealType>()); // - to + max value.
+  }
+}
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> support(const von_mises_distribution<RealType, Policy>& dist)
+{ // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero.
+  return std::pair<RealType, RealType>(dist.mean() - constants::pi<RealType>(),
+                                       dist.mean() + constants::pi<RealType>()); //  [µ-π, µ+π)
+}
+
+#ifdef BOOST_MSVC
+#pragma warning(pop)
+#endif
+
+namespace detail {
+// float version of pdf_impl
+template <class RealType, class Policy>
+inline RealType pdf_impl(const von_mises_distribution<RealType, Policy>& dist, RealType x,
+                         const boost::integral_constant<int, 24>&)
+{
+  RealType mean = dist.mean();
+  RealType conc = dist.concentration();
+
+  BOOST_MATH_STD_USING
+  if(conc < 87)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    return exp(conc * cos(x - mean)) / bessel_i0 / boost::math::constants::two_pi<RealType>();
+  }
+  else  // exp(88) > MAX_FLOAT
+  {
+    // we make use of I0(conc) = exp(conc) * P(conc), with polynomial P
+    // polynomial coefficients from boost/math/special_functions/detail/bessel_i0.hpp
+    static const float P[] = {
+        3.98942280401432677e-01f,
+        4.98677850501790847e-02f,
+        2.80506290907257351e-02f,
+        2.92194053028393074e-02f,
+        4.47422143699726895e-02f,
+    };
+    RealType result = exp(conc * (cos(x - mean) - 1.f));
+    result /= boost::math::tools::evaluate_polynomial(P, RealType(1.f / conc)) / sqrt(conc)
+              * boost::math::constants::two_pi<RealType>();
+    return result;
+  }
+}
+
+// double version of pdf_impl
+template <typename RealType, class Policy>
+inline RealType pdf_impl(const von_mises_distribution<RealType, Policy>& dist, RealType x,
+                         const boost::integral_constant<int, 53>&)
+{
+  RealType mean = dist.mean();
+  RealType conc = dist.concentration();
+
+  BOOST_MATH_STD_USING
+  if(conc < 709)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    return exp(conc * cos(x - mean)) / bessel_i0 / boost::math::constants::two_pi<RealType>();
+  }
+  else // exp(709) > MAX_DOUBLE
+  {
+    // we make use of I0(conc) = exp(conc) * P(conc), with polynomial P
+    // polynomial coefficients from boost/math/special_functions/detail/bessel_i0.hpp
+    static const double P[] = {
+        3.98942280401432905e-01,
+        4.98677850491434560e-02,
+        2.80506308916506102e-02,
+        2.92179096853915176e-02,
+        4.53371208762579442e-02
+    };
+    RealType result = exp(conc * (cos(x - mean) - 1.0));
+    result /= boost::math::tools::evaluate_polynomial(P, RealType(1.0 / conc)) / sqrt(conc)
+              * boost::math::constants::two_pi<RealType>();
+    return result;
+  }
+}
+
+// long double version of pdf_impl
+template <typename RealType, class Policy>
+inline RealType pdf_impl(const von_mises_distribution<RealType, Policy>& dist, RealType x,
+                         const boost::integral_constant<int, 64>&)
+{
+  RealType mean = dist.mean();
+  RealType conc = dist.concentration();
+
+  BOOST_MATH_STD_USING
+  if (conc < 1000)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    return exp(conc * cos(x - mean)) / bessel_i0 / boost::math::constants::two_pi<RealType>();
+  }
+  else
+  {
+    // Bessel I0 over[50, INF]
+    // Max error in interpolated form : 5.587e-20
+    // Max Error found at float80 precision = Poly : 8.776852e-20
+    static const RealType P[] = {
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +3.98942280401432677955074061e-01),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +4.98677850501789875615574058e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +2.80506290908675604202206833e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +2.92194052159035901631494784e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +4.47422430732256364094681137e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +9.05971614435738691235525172e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +2.29180522595459823234266708e-01),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +6.15122547776140254569073131e-01),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +7.48491812136365376477357324e+00),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -2.45569740166506688169730713e+02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +9.66857566379480730407063170e+03),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -2.71924083955641197750323901e+05),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +5.74276685704579268845870586e+06),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -8.89753803265734681907148778e+07),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +9.82590905134996782086242180e+08),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -7.30623197145529889358596301e+09),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +3.27310000726207055200805893e+10),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -6.64365417189215599168817064e+10)
+    };
+    RealType result = exp(conc * (cos(x - mean) - 1.0));
+    result /= boost::math::tools::evaluate_polynomial(P, RealType(1.0 / conc)) / sqrt(conc)
+              * boost::math::constants::two_pi<RealType>();
+    return result;
+  }
+}
+template <typename RealType, class Policy>
+inline RealType pdf_impl(const von_mises_distribution<RealType, Policy>& dist, RealType x,
+                         const boost::integral_constant<int, 113>&)
+{
+  BOOST_MATH_STD_USING  // for ADL of std functions
+  RealType mean = dist.mean();
+  RealType conc = dist.concentration();
+  RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+  return exp(conc * cos(x - mean)) / bessel_i0 / boost::math::constants::two_pi<RealType>();
+}
+} // namespace detail
+
+template <class RealType, class Policy>
+inline RealType pdf(const von_mises_distribution<RealType, Policy>& dist, const RealType& x)
+{
+  BOOST_MATH_STD_USING  // for ADL of std functions
+
+  RealType conc = dist.concentration();
+  RealType mean = dist.mean();
+
+  static const char* function = "boost::math::pdf(const von_mises_distribution<%1%>&, %1%)";
+
+  RealType result = 0;
+  if (false == detail::check_positive_x(function, conc, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, mean, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, x - mean, &result, Policy()))
+    return result;
+  // Below produces MSVC 4127 warnings, so the above used instead.
+  //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
+  //{ // pdf + and - infinity is zero.
+  //  return 0;
+  //}
+  typedef boost::integral_constant<int,
+     ((std::numeric_limits<RealType>::digits == 0) || (std::numeric_limits<RealType>::radix != 2)) ?
+     0 :
+     std::numeric_limits<RealType>::digits <= 24 ?
+     24 :
+     std::numeric_limits<RealType>::digits <= 53 ?
+     53 :
+     std::numeric_limits<RealType>::digits <= 64 ?
+     64 :
+     std::numeric_limits<RealType>::digits <= 113 ?
+     113 : -1
+     > tag_type;
+
+  return detail::pdf_impl(dist, x, tag_type());
+} // pdf
+
+namespace detail {
+
+template <class RealType, class Policy>
+inline RealType cdf_impl(const von_mises_distribution<RealType, Policy>& dist, const RealType& x)
+{
+  BOOST_MATH_STD_USING  // for ADL of std functions
+
+  RealType conc = dist.concentration();
+  RealType mean = dist.mean();
+
+  RealType u = x - mean;
+  if (u <= -boost::math::constants::pi<RealType>())
+    return 0;
+  if (u >= +boost::math::constants::pi<RealType>())
+    return 1;
+
+  // We use the Fortran algorithm designed by Geoffrey W. Hill in
+  // "Algorithm 518: Incomplete Bessel Function I0. The Von Mises Distribution", 1977, ACM
+  // DOI: 10.1145/355744.355753
+  RealType result = 0;
+
+  int digits = std::numeric_limits<RealType>::max_digits10 - 1;
+  RealType ck = ((0.1611*digits - 2.8778)*digits + 18.45)*digits - 35.4;
+  if (conc > ck) {
+    RealType c = 24.0 * conc;
+    RealType v = c - 56;
+    RealType r = sqrt((54.0 / (347.0 / v + 26.0 - c) - 6.0 + c) / 12.0);
+    RealType z = sin(u / 2.0) * r;
+    RealType s = z * z * 2;
+    v = v - s + 3;
+    RealType y = (c - s - s - 16.0) / 3.0;
+    y = ((s + 1.75) * s + 83.5) / v - y;
+    result = boost::math::erf(z - s / (y * y) * z) / 2 + 0.5;
+  }
+  else {
+    RealType v = 0;
+    if(conc > 0) {
+      // extrapolation of the tables given in the paper
+      RealType a1 = (0.33 * digits - 2.6666) * digits + 12;
+      RealType a2 = std::max(0.5, std::min(1.5 - digits / 12, 1.0));
+      RealType a3 = 8;//digits <= 6 ? 3 : (1 << (digits - 5));
+      RealType a4 = digits <= 6 ? 1 : std::pow(1.5, digits - 8);
+
+      int iterations = static_cast<int>(ceil(a1 + conc * a2 - a3 / (conc + a4)));
+      RealType r = 0;
+      RealType z = 2 / conc;
+      for (int j = iterations - 1; j > 0; --j) {
+        RealType sj = sin(j * u);
+        r = 1 / (j * z + r);
+        v = (sj / j + v) * r;
+      }
+    }
+    result = (x - mean + boost::math::constants::pi<RealType>()) / 2;
+    result = (result + v) / boost::math::constants::pi<RealType>();
+  }
+
+  return result <= 0 ? 0 : (1 <= result ? 1 : result);
+}
+} // namespace detail
+
+template <class RealType, class Policy>
+inline RealType cdf(const von_mises_distribution<RealType, Policy>& dist, const RealType& x)
+{
+  RealType conc = dist.concentration();
+  RealType mean = dist.mean();
+  static const char* function = "boost::math::cdf(const von_mises_distribution<%1%>&, %1%)";
+  RealType result = 0;
+  if (false == detail::check_positive_x(function, conc, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, mean, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, x - mean, &result, Policy()))
+    return result;
+
+  return detail::cdf_impl(dist, x);
+} // cdf
+
+template <class RealType, class Policy>
+inline RealType quantile(const von_mises_distribution<RealType, Policy>& dist, const RealType& p)
+{
+  BOOST_MATH_STD_USING  // for ADL of std functions
+
+  RealType conc = dist.concentration();
+  RealType mean = dist.mean();
+  static const char* function
+      = "boost::math::quantile(const von_mises_distribution<%1%>&, %1%)";
+
+  RealType result = 0;
+  if (false == detail::check_positive_x(function, conc, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, mean, &result, Policy()))
+    return result;
+  if (false == detail::check_probability(function, p, &result, Policy()))
+    return result;
+
+  if (p <= 0)
+    return -boost::math::constants::pi<RealType>();
+  if (p >= 1)
+    return +boost::math::constants::pi<RealType>();
+
+  typedef boost::integral_constant<int,
+      ((std::numeric_limits<RealType>::digits == 0)
+          || (std::numeric_limits<RealType>::radix != 2)) ? 0 :
+      std::numeric_limits<RealType>::digits <= 24 ? 24 :
+      std::numeric_limits<RealType>::digits <= 53 ? 53 :
+      std::numeric_limits<RealType>::digits <= 64 ? 64 :
+      std::numeric_limits<RealType>::digits <= 113 ? 113 :
+      -1
+      > tag_type;
+
+  struct step_func {
+    const von_mises_distribution<RealType, Policy>& dist;
+    const RealType p;
+    std::pair<RealType, RealType> operator()(RealType x) {
+      return std::make_pair(detail::cdf_impl(dist, x) - p,            // f(x)
+                            detail::pdf_impl(dist, x, tag_type()));   // f'(x)
+    }
+  };
+  RealType lower = mean - boost::math::constants::pi<RealType>();
+  RealType upper = mean + boost::math::constants::pi<RealType>();
+  RealType zero = boost::math::tools::newton_raphson_iterate(
+      step_func{dist, p}, mean, lower, upper, 15 /* digits */);
+
+  return zero;
+} // quantile
+
+template <class RealType, class Policy>
+inline RealType cdf(const complemented2_type<von_mises_distribution<RealType, Policy>, RealType>& c)
+{
+  RealType conc = c.dist.concentration();
+  RealType mean = c.dist.mean();
+  RealType x = c.param;
+  static const char* function
+      = "boost::math::cdf(const complement(von_mises_distribution<%1%>&), %1%)";
+
+  RealType result = 0;
+  if (false == detail::check_positive_x(function, conc, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, mean, &result, Policy()))
+    return result;
+  if (false == detail::check_angle(function, x - mean, &result, Policy()))
+    return result;
+
+  return detail::cdf_impl(c.dist, 2 * mean - x);
+} // cdf complement
+
+template <class RealType, class Policy>
+inline RealType quantile(const complemented2_type<von_mises_distribution<RealType, Policy>, RealType>& c)
+{
+  BOOST_MATH_STD_USING  // for ADL of std functions
+
+  RealType conc = c.dist.concentration();
+  RealType mean = c.dist.mean();
+  static const char* function
+      = "boost::math::quantile(const complement(von_mises_distribution<%1%>&), %1%)";
+
+  RealType result = 0;
+  if (false == detail::check_positive_x(function, conc, &result, Policy()))
+     return result;
+  if (false == detail::check_angle(function, mean, &result, Policy()))
+     return result;
+  RealType q = c.param;
+  if (false == detail::check_probability(function, q, &result, Policy()))
+     return result;
+
+  if (q <= 0)
+    return +boost::math::constants::pi<RealType>();
+  if (q >= 1)
+    return -boost::math::constants::pi<RealType>();
+
+  typedef boost::integral_constant<int,
+      ((std::numeric_limits<RealType>::digits == 0)
+          || (std::numeric_limits<RealType>::radix != 2)) ? 0 :
+      std::numeric_limits<RealType>::digits <= 24 ? 24 :
+      std::numeric_limits<RealType>::digits <= 53 ? 53 :
+      std::numeric_limits<RealType>::digits <= 64 ? 64 :
+      std::numeric_limits<RealType>::digits <= 113 ? 113 :
+      -1
+      > tag_type;
+
+  struct step_func {
+    const complemented2_type<von_mises_distribution<RealType, Policy>, RealType>& c;
+    std::pair<RealType, RealType> operator()(RealType x) {
+      RealType xc = 2 * c.dist.mean() - x;
+      return std::make_pair(detail::cdf_impl(c.dist, xc) - c.param,    // f(x)
+                           -detail::pdf_impl(c.dist, xc, tag_type())); // f'(x)
+    }
+  };
+  RealType lower = mean - boost::math::constants::pi<RealType>();
+  RealType upper = mean + boost::math::constants::pi<RealType>();
+  RealType zero = boost::math::tools::newton_raphson_iterate(
+      step_func{c}, mean, lower, upper, 15 /* digits */);
+
+  return zero;
+} // quantile
+
+template <class RealType, class Policy>
+inline RealType mean(const von_mises_distribution<RealType, Policy>& dist)
+{
+   return dist.mean();
+}
+
+template <class RealType, class Policy>
+inline RealType standard_deviation(const von_mises_distribution<RealType, Policy>& dist)
+{
+  BOOST_MATH_STD_USING
+  RealType bessel_quot = cyl_bessel_i(1, dist.concentration(), Policy())
+                       / cyl_bessel_i(0, dist.concentration(), Policy());
+  return sqrt(-2 * log(bessel_quot));
+}
+
+template <class RealType, class Policy>
+inline RealType mode(const von_mises_distribution<RealType, Policy>& dist)
+{
+   return dist.mean();
+}
+
+template <class RealType, class Policy>
+inline RealType median(const von_mises_distribution<RealType, Policy>& dist)
+{
+   return dist.mean();
+}
+
+namespace detail {
+// float version of variance_impl
+template <typename RealType, typename Policy>
+inline RealType variance_impl(const von_mises_distribution<RealType, Policy>& dist,
+                              const boost::integral_constant<int, 24>&)
+{
+  RealType conc = dist.concentration();
+  BOOST_MATH_STD_USING
+  if(conc < 7.75)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    RealType bessel_i1 = cyl_bessel_i(1, conc, Policy());
+    return 1 - bessel_i1 / bessel_i0;
+  }
+  else if(conc < 50)
+  {
+    // Polynomial coefficients from
+    // boost/math/special_functions/detail/bessel_i0.hpp and
+    // boost/math/special_functions/detail/bessel_i1.hpp
+    // compute numerator as I0(conc) - I1(conc) from single polynomial
+    static const float P_numer[] = {
+        +5.356107887570000000e-07f,
+        +1.994139882543095464e-01f,
+        +7.683426463016022940e-02f,
+        +4.007722563185265850e-02f,
+        +2.785578524715388070e-01f,
+    };
+    static const float P_denom[] = {
+        +3.98942651588301770e-01f,
+        +4.98327234176892844e-02f,
+        +2.91866904423115499e-02f,
+        +1.35614940793742178e-02f,
+        +1.31409251787866793e-01f,
+    };
+
+    RealType x = 1 / conc;
+    RealType numer = boost::math::tools::evaluate_polynomial(P_numer, x);
+    RealType denom = boost::math::tools::evaluate_polynomial(P_denom, x);
+
+    return numer / denom;
+  }
+  else
+  {
+    static const float P_numer[] = {
+        1.644239196640000000e-07f,
+        1.994490498867993467e-01f,
+        7.569820327857441460e-02f,
+        5.573513685531774810e-02f,
+        1.918908150536447035e-01f
+    };
+    static const float P_denom[] = {
+        3.98942280401432677e-01f,
+        4.98677850501790847e-02f,
+        2.80506290907257351e-02f,
+        2.92194053028393074e-02f,
+        4.47422143699726895e-02f,
+    };
+    RealType x = 1 / conc;
+    RealType numer = boost::math::tools::evaluate_polynomial(P_numer, x);
+    RealType denom = boost::math::tools::evaluate_polynomial(P_denom, x);
+
+    return numer / denom;
+  }
+}
+
+// double version of variance_impl
+template <typename RealType, typename Policy>
+inline RealType variance_impl(const von_mises_distribution<RealType, Policy>& dist,
+                              const boost::integral_constant<int, 53>&)
+{
+  RealType conc = dist.concentration();
+  BOOST_MATH_STD_USING
+  if(conc < 7.75)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    RealType bessel_i1 = cyl_bessel_i(1, conc, Policy());
+    return 1 - bessel_i1 / bessel_i0;
+  }
+  else if(conc < 500)
+  {
+    // Polynomial coefficients from
+    // boost/math/special_functions/detail/bessel_i0.hpp and
+    // boost/math/special_functions/detail/bessel_i1.hpp
+    // compute numerator as I0(conc) - I1(conc) from single polynomial
+    static const double P_numer[] = {
+        -1.55174e-14,
+        +1.994711402218073518e-01,
+        +7.480166592881663552e-02,
+        +7.013008203242116521e-02,
+        +1.016110940936680100e-02,
+        +2.837895300433059925e-01,
+        -6.808807273294442296e+00
+        +4.756438487430168291e+02
+        -2.312449372965164219e+04,
+        +8.645232325622160644e+05,
+        -2.509248065298433807e+07,
+        +5.705709779789331679e+08,
+        -1.021122689535998576e+10,
+        +1.439407686911892518e+11,
+        -1.593043530624297061e+12,
+        +1.373585989454675265e+13,
+        -9.104389306577963414e+13,
+        +4.540402039126762439e+14,
+        -1.645981875199121119e+15,
+        +4.091196019695783875e+15,
+        -6.233158807315033853e+15,
+        +4.389193640817412685e+15,
+    };
+    static const double P_denom[] = {
+        3.98942280401425088e-01,
+        4.98677850604961985e-02,
+        2.80506233928312623e-02,
+        2.92211225166047873e-02,
+        4.44207299493659561e-02,
+        1.30970574605856719e-01,
+        -3.35052280231727022e+00,
+        2.33025711583514727e+02,
+        -1.13366350697172355e+04,
+        4.24057674317867331e+05,
+        -1.23157028595698731e+07,
+        2.80231938155267516e+08,
+        -5.01883999713777929e+09,
+        7.08029243015109113e+10,
+        -7.84261082124811106e+11,
+        6.76825737854096565e+12,
+        -4.49034849696138065e+13,
+        2.24155239966958995e+14,
+        -8.13426467865659318e+14,
+        2.02391097391687777e+15,
+        -3.08675715295370878e+15,
+        2.17587543863819074e+15
+    };
+    RealType x = 1 / conc;
+    RealType numer = boost::math::tools::evaluate_polynomial(P_numer, x);
+    RealType denom = boost::math::tools::evaluate_polynomial(P_denom, x);
+
+    return numer / denom;
+  }
+  else
+  {
+    static const double P_numer[] = {
+        +1.423e-15,
+        +1.994711401959018717e-01,
+        +7.480168411736836931e-02,
+        +7.012212565916144652e-02,
+        +1.037734243240472200e-01,
+    };
+    static const double P_denom[] = {
+        3.98942280401432905e-01,
+        4.98677850491434560e-02,
+        2.80506308916506102e-02,
+        2.92179096853915176e-02,
+        4.53371208762579442e-02,
+    };
+    RealType x = 1 / conc;
+    RealType numer = boost::math::tools::evaluate_polynomial(P_numer, x);
+    RealType denom = boost::math::tools::evaluate_polynomial(P_denom, x);
+
+    return numer / denom;
+  }
+}
+
+// long double version of variance_impl
+template <typename RealType, class Policy>
+inline RealType variance_impl(const von_mises_distribution<RealType, Policy>& dist,
+                              const boost::integral_constant<int, 64>&)
+{
+  BOOST_MATH_STD_USING
+  RealType conc = dist.concentration();
+  if (conc < 50)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    RealType bessel_i1 = cyl_bessel_i(1, conc, Policy());
+    return 1 - bessel_i1 / bessel_i0;
+  }
+  else
+  {
+    static const RealType P[] = {
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +3.98942280401432677955074061e-01),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +4.98677850501789875615574058e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +2.80506290908675604202206833e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +2.92194052159035901631494784e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +4.47422430732256364094681137e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +9.05971614435738691235525172e-02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +2.29180522595459823234266708e-01),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +6.15122547776140254569073131e-01),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +7.48491812136365376477357324e+00),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -2.45569740166506688169730713e+02),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +9.66857566379480730407063170e+03),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -2.71924083955641197750323901e+05),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +5.74276685704579268845870586e+06),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -8.89753803265734681907148778e+07),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +9.82590905134996782086242180e+08),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -7.30623197145529889358596301e+09),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, +3.27310000726207055200805893e+10),
+        BOOST_MATH_BIG_CONSTANT(RealType, 64, -6.64365417189215599168817064e+10)
+    };
+    return 0;
+  }
+}
+
+// quad version of variance_impl
+template <typename RealType, class Policy>
+inline RealType variance_impl(const von_mises_distribution<RealType, Policy>& dist,
+                              const boost::integral_constant<int, 113>&)
+{
+  BOOST_MATH_STD_USING
+  RealType conc = dist.concentration();
+  if (conc < 100)
+  {
+    RealType bessel_i0 = cyl_bessel_i(0, conc, Policy());
+    RealType bessel_i1 = cyl_bessel_i(1, conc, Policy());
+    return 1 - bessel_i1 / bessel_i0;
+  }
+  else
+  {
+    // Polynomial for Bessel I0 / exp(conc) / sqrt(conc)
+    static const RealType P_denom[] = {
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.9894228040143267793994605993438166526772e-01),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.9867785050179084742493257495245185241487e-02),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.8050629090725735167652437695397756897920e-02),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.9219405302839307466358297347675795965363e-02),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.4742214369972689474366968442268908028204e-02),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.0602984099194778006610058410222616383078e-02),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.2839502241666629677015839125593079416327e-01),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.8926354981801627920292655818232972385750e-01),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.4231921590621824187100989532173995000655e+00),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.7264260959693775207585700654645245723497e+00),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.3890136225398811195878046856373030127018e+01),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.1999720924619285464910452647408431234369e+02),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.2076909538525038580501368530598517194748e+03),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.5684635141332367730007149159063086133399e+03),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.5178192543258299267923025833141286569141e+04),
+      BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.2966297919851965784482163987240461837728e+05)
+    };
+
+    // Polynomial for (Bessel I0 - Bessel I1) / exp(conc) / sqrt(x)
+    static const RealType P_numer[] = {
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, -3.368165e-34),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +0.1994711402007163389699730299733589146073),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +0.07480167757526862711373984952175456888896),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +0.07012657272681433791923412617430580227103),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +0.10226791855993757596915805134093796837369),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +0.2013399646648772644282448264813045181469),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +0.4983164125454637874163933874417571110056),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +1.4845676457582822590839158984567308297366),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +5.169476606935535670414552625141409318434),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +20.59713743665130419014001937211862931161),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +92.40031163861578044111910646492625263225),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +460.9440321063085921197536056693132597443),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +2.520575547528944544570101030955801999019e+03),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +1.5734053646329490893326466550032992462076e+04),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +7.319778356894459435808347175389511056370e+04),
+       BOOST_MATH_BIG_CONSTANT(RealType, 113, +1.2997438696903014448182029282439919466883e+06),
+    };
+    RealType x = 1 / conc;
+    RealType numer = boost::math::tools::evaluate_polynomial(P_numer, x);
+    RealType denom = boost::math::tools::evaluate_polynomial(P_denom, x);
+
+    return numer / denom;
+  }
+}
+} // namespace detail
+
+template <class RealType, class Policy>
+inline RealType variance(const von_mises_distribution<RealType, Policy>& dist)
+{
+
+  typedef boost::integral_constant<int,
+      ((std::numeric_limits<RealType>::digits == 0)
+          || (std::numeric_limits<RealType>::radix != 2)) ? 0 :
+      std::numeric_limits<RealType>::digits <= 24 ? 24 :
+      std::numeric_limits<RealType>::digits <= 53 ? 53 :
+      std::numeric_limits<RealType>::digits <= 64 ? 64 :
+      std::numeric_limits<RealType>::digits <= 113 ? 113 :
+      -1
+      > tag_type;
+
+  return detail::variance_impl(dist, tag_type());
+}
+
+template <class RealType, class Policy>
+inline RealType skewness(const von_mises_distribution<RealType, Policy>& /*dist*/)
+{
+   return 0;
+}
+
+template <class RealType, class Policy>
+inline RealType entropy(const von_mises_distribution<RealType, Policy> & dist)
+{
+   BOOST_MATH_STD_USING
+   RealType arg = constants::two_pi<RealType>() * cyl_bessel_i(0, dist.concentration(), Policy());
+   RealType bessel_quot = cyl_bessel_i(1, dist.concentration(), Policy())
+                        / cyl_bessel_i(0, dist.concentration(), Policy());
+   return log(arg) - dist.concentration() * bessel_quot;
+}
+
+} // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include <boost/math/distributions/detail/derived_accessors.hpp>
+
+#endif // BOOST_MATH_DISTRIBUTIONS_VON_MISES_HPP
+
+
diff --git a/reporting/accuracy/von_mises_ulps.cpp b/reporting/accuracy/von_mises_ulps.cpp
new file mode 100644
index 0000000000..a63b494bbf
--- /dev/null
+++ b/reporting/accuracy/von_mises_ulps.cpp
@@ -0,0 +1,81 @@
+﻿#include <string>
+
+#include <boost/math/distributions/von_mises.hpp>
+#include <boost/math/tools/ulps_plot.hpp>
+
+using precise_real = long double;
+
+template <typename CoarseReal>
+void generate_ulps_plot_pdf(CoarseReal concentration)
+{
+    auto hi_conc = static_cast<precise_real>(concentration);
+    auto high_precision = [hi_conc](precise_real x)
+    {
+        boost::math::von_mises_distribution<precise_real> dist(0, hi_conc);
+        return boost::math::pdf(dist, x);
+    };
+
+    auto low_precision = [concentration](CoarseReal x)
+    {
+        boost::math::von_mises_distribution<CoarseReal> dist(0, concentration);
+        return boost::math::pdf(dist, x);
+    };
+
+    using hp_func = decltype (high_precision);
+
+    boost::math::tools::ulps_plot<hp_func, precise_real, CoarseReal> plot(
+                high_precision, 0, boost::math::constants::pi<CoarseReal>());
+    plot.add_fn(low_precision);
+    std::string filename = "von_mises_ulps_pdf_"
+                           + std::to_string(static_cast<int>(concentration))
+                           + typeid(CoarseReal).name()
+                           + ".svg";
+    plot.write(filename);
+}
+
+template <typename CoarseReal>
+void generate_ulps_plot_cdf(CoarseReal concentration)
+{
+    auto hi_conc = static_cast<precise_real>(concentration);
+    auto high_precision = [hi_conc](precise_real x)
+    {
+        boost::math::von_mises_distribution<precise_real> dist(0, hi_conc);
+        return boost::math::cdf(dist, x);
+    };
+
+    auto low_precision = [concentration](CoarseReal x)
+    {
+        boost::math::von_mises_distribution<CoarseReal> dist(0, concentration);
+        return boost::math::cdf(dist, x);
+    };
+
+    using hp_func = decltype (high_precision);
+
+    auto pi = boost::math::constants::pi<CoarseReal>();
+    boost::math::tools::ulps_plot<hp_func, precise_real, CoarseReal> plot(
+                high_precision, -pi, +pi);
+    plot.add_fn(low_precision);
+    std::string filename = "von_mises_ulps_cdf_"
+                           + std::to_string(static_cast<int>(concentration))
+                           + typeid(CoarseReal).name()
+                           + ".svg";
+    plot.write(filename);
+}
+
+void generate_ulps_plots(double concentration)
+{
+    float fconc = static_cast<float>(concentration);
+    generate_ulps_plot_pdf<float>(fconc);
+    generate_ulps_plot_cdf<float>(fconc);
+
+    generate_ulps_plot_pdf<double>(concentration);
+    generate_ulps_plot_cdf<double>(concentration);
+}
+
+int main()
+{
+    generate_ulps_plots(4);
+    generate_ulps_plots(64);
+
+    return 0;
+}
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index a98f8dc310..24350f0c3e 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -793,6 +793,9 @@ test-suite distribution_tests :
          [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>"-Bstatic -lquadmath -Bdynamic" ] ]
    [ run test_triangular.cpp pch ../../test/build//boost_unit_test_framework  ]
    [ run test_uniform.cpp pch ../../test/build//boost_unit_test_framework  ]
+   [ run test_von_mises.cpp pch ../../test/build//boost_unit_test_framework : : :
+         [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>"-Bstatic -lquadmath -Bdynamic" ]
+   ]
    [ run test_weibull.cpp ../../test/build//boost_unit_test_framework  ]
 
    [ run  compile_test/dist_bernoulli_incl_test.cpp compile_test_main  ]
diff --git a/test/test_von_mises.cpp b/test/test_von_mises.cpp
new file mode 100644
index 0000000000..3a89d17650
--- /dev/null
+++ b/test/test_von_mises.cpp
@@ -0,0 +1,397 @@
+// Copyright Philipp C. J. Münster 2020.
+// Copyright Paul A. Bristow 2010.
+// Copyright John Maddock 2007.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+// test_von_mises.cpp
+
+// https://en.wikipedia.org/wiki/Von_Mises_distribution
+// From MathWorld--A Wolfram Web Resource.
+// http://mathworld.wolfram.com/VonMisesDistribution.html
+
+#ifdef _MSC_VER
+#  pragma warning (disable: 4127) // conditional expression is constant
+// caused by using   if(std::numeric_limits<RealType>::has_infinity)
+// and   if (std::numeric_limits<RealType>::has_quiet_NaN)
+#endif
+
+#include <boost/cstdfloat.hpp>
+#include <boost/multiprecision/float128.hpp>
+   using boost::multiprecision::float128;
+#include <boost/math/concepts/real_concept.hpp> // for real_concept
+
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp> // Boost.Test
+#include <boost/test/tools/floating_point_comparison.hpp>
+
+#include <boost/math/distributions/von_mises.hpp>
+   using boost::math::von_mises_distribution;
+#include <boost/math/tools/test.hpp>
+
+#include "math_unit_test.hpp"
+#include "pch.hpp"
+#include "test_out_of_range.hpp"
+
+#include <iostream>
+#include <iomanip>
+   using std::cout;
+   using std::endl;
+   using std::setprecision;
+#include <limits>
+   using std::numeric_limits;
+
+template <class RealType>
+void check_von_mises(RealType mean, RealType conc, RealType x, RealType p, RealType q, RealType tol)
+{
+  BOOST_CHECK_CLOSE(
+      ::boost::math::cdf(
+          von_mises_distribution<RealType>(mean, conc),      // distribution.
+          x),                                                // random variable.
+      p,                                                     // probability.
+      tol);                                                  // %tolerance.
+  BOOST_CHECK_CLOSE(
+      ::boost::math::cdf(
+          complement(
+              von_mises_distribution<RealType>(mean, conc),  // distribution.
+              x)),                                           // random variable.
+      q,                                                     // probability complement.
+      tol);                                                  // %tolerance.
+  BOOST_CHECK_CLOSE(
+      ::boost::math::quantile(
+          von_mises_distribution<RealType>(mean, conc),      // distribution.
+          p),                                                // probability.
+      x,                                                     // random variable.
+      tol);                                                  // %tolerance.
+   BOOST_CHECK_CLOSE(
+      ::boost::math::quantile(
+          complement(
+              von_mises_distribution<RealType>(mean, conc),  // distribution.
+              q)),                                           // probability complement.
+      x,                                                     // random variable.
+      tol);                                                  // %tolerance.
+}
+
+template <class RealType>
+void test_spots(RealType)
+{
+  // Basic sanity checks
+  // Check some bad parameters to the distribution,
+#ifndef BOOST_NO_EXCEPTIONS
+  BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType> nbad1(0, -1), std::domain_error); // negative conc
+#else
+  BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType>(0, -1), std::domain_error); // negative conc
+#endif
+
+  // Tests on extreme values of random variate x, if has std::numeric_limits infinity etc.
+  von_mises_distribution<RealType> N01;
+  if(std::numeric_limits<RealType>::has_infinity)
+  {
+    BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::infinity()), std::domain_error);             // x = + infinity, pdf = 0
+    BOOST_MATH_CHECK_THROW(pdf(N01, -std::numeric_limits<RealType>::infinity()), std::domain_error);             // x = - infinity, pdf = 0
+    BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::infinity()), std::domain_error);             // x = + infinity, cdf = 1
+    BOOST_MATH_CHECK_THROW(cdf(N01, -std::numeric_limits<RealType>::infinity()), std::domain_error);             // x = - infinity, cdf = 0
+    BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), std::domain_error); // x = + infinity, c cdf = 0
+    BOOST_MATH_CHECK_THROW(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), std::domain_error); // x = - infinity, c cdf = 1
+
+#ifndef BOOST_NO_EXCEPTIONS
+    BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
+    BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
+    BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite conc
+#else
+    BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType>(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
+    BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType>(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
+    BOOST_MATH_CHECK_THROW(boost::math::von_mises_distribution<RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite conc
+#endif
+  }
+
+  if (std::numeric_limits<RealType>::has_quiet_NaN)
+  {
+    // No longer allow x to be NaN, then these tests should throw.
+    BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
+    BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
+    BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
+    BOOST_MATH_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
+    BOOST_MATH_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
+  }
+
+  //
+  // Tests for PDF: we know that the peak value is at e/(2*pi*I0(1)
+  //
+  RealType tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(), static_cast<RealType>(0)),
+      static_cast<RealType>(0.34171048862346315949457814754706159394027L),  // e/(2*pi*I0(1))
+      tolerance);
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 0), static_cast<RealType>(3)),
+      static_cast<RealType>(0.15915494309189533576888376337251L),           // 1/(2*pi)
+      tolerance);
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3), static_cast<RealType>(3)),
+      static_cast<RealType>(0.34171048862346315949457814754706159394027L),  // e/(2*pi*I0(1))
+      tolerance);
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 5), static_cast<RealType>(3)),
+      static_cast<RealType>(0.86713652854235200257351846969777045343907L),  // e^5/(2*pi*I0(5))
+      tolerance);
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 25), static_cast<RealType>(3)),
+      static_cast<RealType>(1.98455543847726689510475504795539869409664L),  // e^25/(2*pi*I0(25))
+      tolerance);
+	// edge case for single point precision
+	BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 86), static_cast<RealType>(3)),
+      static_cast<RealType>(3.69423343123704539549725123346713237943413L),
+      tolerance);
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 87), static_cast<RealType>(3)),
+      static_cast<RealType>(3.71571226458759536792289974309199255119626L),
+      tolerance);
+	// edge case for double point precision
+  BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 708), static_cast<RealType>(3)),
+      static_cast<RealType>(10.6132883625399035032551439553585260831760L),
+      tolerance);
+	BOOST_CHECK_CLOSE(
+      pdf(von_mises_distribution<RealType>(3, 709), static_cast<RealType>(3)),
+      static_cast<RealType>(10.6207836264247647802343430545802569228891L),
+      tolerance);
+
+  tolerance = 2e-3f; // 2e-5 (as %)
+
+  cout << "Tolerance for type " << typeid(RealType).name()
+       << " is " << tolerance << " %" << endl;
+
+  // test CDF for mean and interval edges
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(1),
+      static_cast<RealType>(0),
+      static_cast<RealType>(0.5L),
+      static_cast<RealType>(0.5L),
+      tolerance);
+
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(1),
+      static_cast<RealType>(-boost::math::constants::pi<RealType>()),
+      static_cast<RealType>(0.0L),
+      static_cast<RealType>(1.0L),
+      tolerance);
+
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(1),
+      static_cast<RealType>(boost::math::constants::pi<RealType>()),
+      static_cast<RealType>(1.0L),
+      static_cast<RealType>(0.0L),
+      tolerance);
+
+  // test CDF for low concentrations
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(1),
+      static_cast<RealType>(1),
+      static_cast<RealType>(0.794355307434683479987678129735260058645499262629455722769L),
+      static_cast<RealType>(0.205644692565316520012321870264739941354500737370544277230L),
+      tolerance);
+
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(1),
+      static_cast<RealType>(-1),
+      static_cast<RealType>(0.205644692565316520012321870264739941354500737370544277230L),
+      static_cast<RealType>(0.794355307434683479987678129735260058645499262629455722769L),
+      tolerance);
+
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(5),
+      static_cast<RealType>(1),
+      static_cast<RealType>(0.98096204546814689054581384796251763480020360394758184271L),
+      static_cast<RealType>(0.01903795453185310945418615203748236519979639605241815729L),
+      tolerance);
+
+  check_von_mises(
+      static_cast<RealType>(0),
+      static_cast<RealType>(5),
+      static_cast<RealType>(-1),
+      static_cast<RealType>(0.01903795453185310945418615203748236519979639605241815729L),
+      static_cast<RealType>(0.98096204546814689054581384796251763480020360394758184271L),
+      tolerance);
+
+  // test CDF for high concentrations
+  //~ check_von_mises(
+      //~ static_cast<RealType>(0),
+      //~ static_cast<RealType>(25),
+      //~ static_cast<RealType>(1),
+      //~ static_cast<RealType>(0.999999062404464440452233504489299782776166264467210572765L),
+      //~ static_cast<RealType>(9.37595535559547766495510700217223833735532789427234e-7L),
+      //~ tolerance);
+
+  //~ check_von_mises(
+      //~ static_cast<RealType>(0),
+      //~ static_cast<RealType>(25),
+      //~ static_cast<RealType>(-1),
+      //~ static_cast<RealType>(9.37595535559547766495510700217223833735532789427234e-7L),
+      //~ static_cast<RealType>(0.999999062404464440452233504489299782776166264467210572765L),
+      //~ tolerance);
+
+  //~ check_von_mises(
+      //~ static_cast<RealType>(0),
+      //~ static_cast<RealType>(125),
+      //~ static_cast<RealType>(1),
+      //~ static_cast<RealType>(0.99999999999999999996645363431349332910951002333081490389L),
+      //~ static_cast<RealType>(3.3546365686506670890489976669185096109e-20L),
+      //~ tolerance);
+
+  //~ check_von_mises(
+      //~ static_cast<RealType>(0),
+      //~ static_cast<RealType>(125),
+      //~ static_cast<RealType>(-1),
+      //~ static_cast<RealType>(3.3546365686506670890489976669185096109e-20L),
+      //~ static_cast<RealType>(0.99999999999999999996645363431349332910951002333081490389L),
+      //~ tolerance);
+
+
+  RealType tol2 = boost::math::tools::epsilon<RealType>() * 500;
+  von_mises_distribution<RealType> dist(2, 3);
+  RealType x = static_cast<RealType>(0.125);
+
+  BOOST_MATH_STD_USING // ADL of std math lib names
+
+  // mean:
+  BOOST_CHECK_CLOSE(
+       mean(dist)
+       , static_cast<RealType>(2), tol2);
+  // variance:
+  BOOST_CHECK_CLOSE(
+       variance(von_mises_distribution<RealType>(2, 0))
+       , static_cast<RealType>(1), tol2);
+  BOOST_CHECK_CLOSE(
+       variance(von_mises_distribution<RealType>(2, 1))
+       , static_cast<RealType>(0.553610034103465492952318204807357330223746852599612177138L), tol2);
+  BOOST_CHECK_CLOSE(
+       variance(von_mises_distribution<RealType>(2, 5))
+       , static_cast<RealType>(0.106616862955914778412994992775050827245562823701700738786L), tol2);
+  //~ BOOST_CHECK_CLOSE(
+       //~ variance(von_mises_distribution<RealType>(2, 25))
+       //~ , static_cast<RealType>(0.020208546509484068780303296944566388571293465011951716357L), tol2);
+  //~ BOOST_CHECK_CLOSE(
+       //~ variance(von_mises_distribution<RealType>(2, 125))
+       //~ , static_cast<RealType>(0.004008064813593637057963834031301840442156903531539609019L), tol2);
+
+  // std deviation:
+  BOOST_CHECK_CLOSE(
+       standard_deviation(dist)
+       , static_cast<RealType>(0.649213658343262740252572725779410261163523458085389547123L), tol2);
+  // hazard:
+  BOOST_CHECK_CLOSE(
+       hazard(dist, x)
+       , pdf(dist, x) / cdf(complement(dist, x)), tol2);
+  // cumulative hazard:
+  BOOST_CHECK_CLOSE(
+       chf(dist, x)
+       , -log(cdf(complement(dist, x))), tol2);
+  // coefficient_of_variation:
+  BOOST_CHECK_CLOSE(
+       coefficient_of_variation(dist)
+       , standard_deviation(dist) / mean(dist), tol2);
+  // mode:
+  BOOST_CHECK_CLOSE(
+       mode(dist)
+       , static_cast<RealType>(2), tol2);
+
+  BOOST_CHECK_CLOSE(
+       median(dist)
+       , static_cast<RealType>(2), tol2);
+
+  // skewness:
+  BOOST_CHECK_CLOSE(
+       skewness(dist)
+       , static_cast<RealType>(0), tol2);
+
+  BOOST_CHECK_CLOSE(
+       entropy(dist)
+       , 0.993228806353252817873771736349142645476889275244864748502L, tol2);
+
+  von_mises_distribution<RealType> norm01(0, 1); // Test default (0, 1)
+  BOOST_CHECK_CLOSE(
+       mean(norm01),
+       static_cast<RealType>(0), 0); // Mean == zero
+
+  von_mises_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
+  BOOST_CHECK_CLOSE(
+       mean(defsd_norm01),
+       static_cast<RealType>(0), 0); // Mean == zero
+
+  von_mises_distribution<RealType> def_norm01; // Test default (0, sd = 1)
+  BOOST_CHECK_CLOSE(
+       mean(def_norm01),
+       static_cast<RealType>(0), 0); // Mean == zero
+
+  // Error tests:
+  check_out_of_range<boost::math::von_mises_distribution<RealType> >(0, 1); // (All) valid constructor parameter values.
+
+  BOOST_MATH_CHECK_THROW(quantile(von_mises_distribution<RealType>(0, 1), -1), std::domain_error);
+  BOOST_MATH_CHECK_THROW(quantile(von_mises_distribution<RealType>(0, 1), 2), std::domain_error);
+} // template <class RealType>void test_spots(RealType)
+
+template <typename RealType>
+void test_symmetry(RealType)
+{
+	RealType const pi = boost::math::constants::pi<RealType>();
+	RealType delta = 1.0 / (1 << 4);
+  for (RealType mean = 0; mean < pi; mean += delta) {
+    for (RealType conc = 0; conc < 100; conc = (conc + 1) * 1.5 - 1) {
+      von_mises_distribution<RealType> dist(mean, conc);
+      for (RealType x = 0; x < pi; x += delta) {
+        CHECK_ULP_CLOSE(pdf(dist, mean + x),
+                        pdf(dist, mean - x), 2);
+        CHECK_ULP_CLOSE(cdf(dist, mean + x) - static_cast<RealType>(0.5),
+                        static_cast<RealType>(0.5) - cdf(dist, mean - x), 32);
+      }
+    }
+  }
+}
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+  // Check that we can generate von_mises distribution using the two convenience methods:
+  boost::math::von_mises myf1(1., 2);       // Using typedef
+  von_mises_distribution<> myf2(1., 2);     // Using default RealType double.
+  boost::math::von_mises myn01;             // Use default values.
+  // Note NOT myn01() as the compiler will interpret as a function!
+
+  // Check the synonyms, provided to allow generic use of find_location and find_scale.
+  BOOST_CHECK_EQUAL(myn01.mean(), myn01.location());
+  BOOST_CHECK_EQUAL(myn01.concentration(), myn01.scale());
+
+  // Basic sanity-check spot values.
+  // (Parameter value, arbitrarily zero, only communicates the floating point type).
+  test_spots(0.0F);   // Test float. OK at decdigits = 0 tolerance = 0.0001 %
+  test_spots(0.0);    // Test double. OK at decdigits 7, tolerance = 1e07 %
+  test_spots(0.0L); // Test long double.
+  test_spots(static_cast<float128>(0));
+
+  // Check symmetry of PDF and CDF
+  test_symmetry(0.0F);
+  test_symmetry(0.0);
+  test_symmetry(0.0L);
+  test_symmetry(static_cast<float128>(0));
+} // BOOST_AUTO_TEST_CASE( test_main )
+
+/*
+./test_von_mises.exe
+Output:
+
+Running 1 test case...
+Tolerance for type f is 0.002 %
+Tolerance for type d is 0.002 %
+Tolerance for type e is 0.002 %
+
+*** No errors detected */
