Patchwork Implement Pareto distribution as an extension.

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Submitter Ed Smith-Rowland
Date Sept. 21, 2012, 12:36 p.m.
Message ID <505C5F69.2080007@verizon.net>
Download mbox | patch
Permalink /patch/185725/
State New
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Comments

Ed Smith-Rowland - Sept. 21, 2012, 12:36 p.m.
On 09/21/2012 05:33 AM, Paolo Carlini wrote:
> On 09/21/2012 11:02 AM, Ulrich Drepper wrote:
>> On Thu, Sep 20, 2012 at 6:17 AM, Paolo Carlini 
>> <paolo.carlini@oracle.com> wrote:
>>> Patch looks generally Ok to me. If Ulrich and the other interested 
>>> parties
>>> don't have anything to add over the next 24 hrs or so, let's go 
>>> ahead and
>>> thanks again!
>> Unfortunately I won't have any time until Wednesday.  I'm sure there's
>> nothing in the patch which if necessary cannot be fixed.
> Good, Ok then we can commit it.
>> For testing we might want to utilize R for testing, if available.  Or
>> specific test generation.  There are some things that can be done.
>> But I have some other patches to contribute first.  Next week...
> Ok...
>
> Paolo.
>
Committed.
Ed
2012-09-21  Edward Smith-Rowland  <3dw4rd@verizon.net>

	* include/ext/random: Add __gnu_cxx::pareto_distribution<> class.
	* include/ext/random.tcc: Add out-of-line functions for
	__gnu_cxx::pareto_distribution<>.
	* testsuite/ext/random/pareto_distribution/operators/equal.cc: New file.
	* testsuite/ext/random/pareto_distribution/operators/serialize.cc:
	New file.
	* testsuite/ext/random/pareto_distribution/operators/inequal.cc:
	New file.
	* testsuite/ext/random/pareto_distribution/cons/parms.cc: New file.
	* testsuite/ext/random/pareto_distribution/cons/default.cc: New file.
	* testsuite/ext/random/pareto_distribution/requirements/typedefs.cc:
	New file.
	* testsuite/ext/random/pareto_distribution/requirements/
	explicit_instantiation/1.cc: New file.

Patch

Index: include/ext/random
===================================================================
--- include/ext/random	(revision 191434)
+++ include/ext/random	(working copy)
@@ -1360,6 +1360,242 @@ 
 	       const nakagami_distribution<_RealType>& __d2)
     { return !(__d1 == __d2); }
 
+
+  /**
+   * @brief A Pareto continuous distribution for random numbers.
+   *
+   * The formula for the Pareto cumulative probability function is
+   * @f[
+   *     P(x|\alpha,\mu) = 1 - \left(\frac{\mu}{x}\right)^\alpha
+   * @f]
+   * The formula for the Pareto probability density function is
+   * @f[
+   *     p(x|\alpha,\mu) = \frac{\alpha + 1}{\mu}
+   *                       \left(\frac{\mu}{x}\right)^{\alpha + 1}
+   * @f]
+   * where @f$x >= \mu@f$ and @f$\mu > 0@f$, @f$\alpha > 0@f$.
+   *
+   * <table border=1 cellpadding=10 cellspacing=0>
+   * <caption align=top>Distribution Statistics</caption>
+   * <tr><td>Mean</td><td>@f$\alpha \mu / (\alpha - 1)@f$
+   *              for @f$\alpha > 1@f$</td></tr>
+   * <tr><td>Variance</td><td>@f$\alpha \mu^2 / [(\alpha - 1)^2(\alpha - 2)]@f$
+   *              for @f$\alpha > 2@f$</td></tr>
+   * <tr><td>Range</td><td>@f$[\mu, \infty)@f$</td></tr>
+   * </table>
+   */
+  template<typename _RealType = double>
+    class
+    pareto_distribution
+    {
+      static_assert(std::is_floating_point<_RealType>::value,
+		    "template argument not a floating point type");
+
+    public:
+      /** The type of the range of the distribution. */
+      typedef _RealType result_type;
+      /** Parameter type. */
+      struct param_type
+      {
+	typedef pareto_distribution<result_type> distribution_type;
+
+	param_type(result_type __alpha = result_type(1),
+		   result_type __mu = result_type(1))
+	: _M_alpha(__alpha), _M_mu(__mu)
+	{
+	  _GLIBCXX_DEBUG_ASSERT(_M_alpha > result_type(0));
+	  _GLIBCXX_DEBUG_ASSERT(_M_mu > result_type(0));
+	}
+
+	result_type
+	alpha() const
+	{ return _M_alpha; }
+
+	result_type
+	mu() const
+	{ return _M_mu; }
+
+	friend bool
+	operator==(const param_type& __p1, const param_type& __p2)
+	{ return __p1._M_alpha == __p2._M_alpha && __p1._M_mu == __p2._M_mu; }
+
+      private:
+	void _M_initialize();
+
+	result_type _M_alpha;
+	result_type _M_mu;
+      };
+
+      /**
+       * @brief Constructors.
+       */
+      explicit
+      pareto_distribution(result_type __alpha = result_type(1),
+			  result_type __mu = result_type(1))
+      : _M_param(__alpha, __mu),
+	_M_ud()
+      { }
+
+      explicit
+      pareto_distribution(const param_type& __p)
+      : _M_param(__p),
+	_M_ud()
+      { }
+
+      /**
+       * @brief Resets the distribution state.
+       */
+      void
+      reset()
+      {
+	_M_ud.reset();
+      }
+
+      /**
+       * @brief Return the parameters of the distribution.
+       */
+      result_type
+      alpha() const
+      { return _M_param.alpha(); }
+
+      result_type
+      mu() const
+      { return _M_param.mu(); }
+
+      /**
+       * @brief Returns the parameter set of the distribution.
+       */
+      param_type
+      param() const
+      { return _M_param; }
+
+      /**
+       * @brief Sets the parameter set of the distribution.
+       * @param __param The new parameter set of the distribution.
+       */
+      void
+      param(const param_type& __param)
+      { _M_param = __param; }
+
+      /**
+       * @brief Returns the greatest lower bound value of the distribution.
+       */
+      result_type
+      min() const
+      { return this->mu(); }
+
+      /**
+       * @brief Returns the least upper bound value of the distribution.
+       */
+      result_type
+      max() const
+      { return std::numeric_limits<result_type>::max(); }
+
+      /**
+       * @brief Generating functions.
+       */
+      template<typename _UniformRandomNumberGenerator>
+	result_type
+	operator()(_UniformRandomNumberGenerator& __urng)
+	{
+	  return this->mu() * std::pow(this->_M_ud(__urng),
+				       -result_type(1) / this->alpha());
+	}
+
+      template<typename _UniformRandomNumberGenerator>
+	result_type
+	operator()(_UniformRandomNumberGenerator& __urng,
+		   const param_type& __p)
+        {
+	  return __p.mu() * std::pow(this->_M_ud(__urng),
+					   -result_type(1) / __p.alpha());
+	}
+
+      template<typename _ForwardIterator,
+	       typename _UniformRandomNumberGenerator>
+	void
+	__generate(_ForwardIterator __f, _ForwardIterator __t,
+		   _UniformRandomNumberGenerator& __urng)
+	{ this->__generate(__f, __t, __urng, this->param()); }
+
+      template<typename _ForwardIterator,
+	       typename _UniformRandomNumberGenerator>
+	void
+	__generate(_ForwardIterator __f, _ForwardIterator __t,
+		   _UniformRandomNumberGenerator& __urng,
+		   const param_type& __p)
+	{ this->__generate_impl(__f, __t, __urng, __p); }
+
+      template<typename _UniformRandomNumberGenerator>
+	void
+	__generate(result_type* __f, result_type* __t,
+		   _UniformRandomNumberGenerator& __urng,
+		   const param_type& __p)
+	{ this->__generate_impl(__f, __t, __urng, __p); }
+
+      /**
+       * @brief Return true if two Pareto distributions have
+       *        the same parameters and the sequences that would
+       *        be generated are equal.
+       */
+      friend bool
+      operator==(const pareto_distribution& __d1,
+		 const pareto_distribution& __d2)
+      { return (__d1.param() == __d2.param()
+		&& __d1._M_ud == __d2._M_ud); }
+
+      /**
+       * @brief Inserts a %pareto_distribution random number distribution
+       * @p __x into the output stream @p __os.
+       *
+       * @param __os An output stream.
+       * @param __x  A %pareto_distribution random number distribution.
+       *
+       * @returns The output stream with the state of @p __x inserted or in
+       * an error state.
+       */
+      template<typename _RealType1, typename _CharT, typename _Traits>
+	friend std::basic_ostream<_CharT, _Traits>&
+	operator<<(std::basic_ostream<_CharT, _Traits>&,
+		   const pareto_distribution<_RealType1>&);
+
+      /**
+       * @brief Extracts a %pareto_distribution random number distribution
+       * @p __x from the input stream @p __is.
+       *
+       * @param __is An input stream.
+       * @param __x A %pareto_distribution random number
+       *            generator engine.
+       *
+       * @returns The input stream with @p __x extracted or in an error state.
+       */
+      template<typename _RealType1, typename _CharT, typename _Traits>
+	friend std::basic_istream<_CharT, _Traits>&
+	operator>>(std::basic_istream<_CharT, _Traits>&,
+		   pareto_distribution<_RealType1>&);
+
+    private:
+      template<typename _ForwardIterator,
+	       typename _UniformRandomNumberGenerator>
+	void
+	__generate_impl(_ForwardIterator __f, _ForwardIterator __t,
+			_UniformRandomNumberGenerator& __urng,
+			const param_type& __p);
+
+      param_type _M_param;
+
+      std::uniform_real_distribution<result_type> _M_ud;
+    };
+
+  /**
+   * @brief Return true if two Pareto distributions are not equal.
+   */
+  template<typename _RealType>
+    inline bool
+    operator!=(const pareto_distribution<_RealType>& __d1,
+	       const pareto_distribution<_RealType>& __d2)
+    { return !(__d1 == __d2); }
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace __gnu_cxx
 
Index: include/ext/random.tcc
===================================================================
--- include/ext/random.tcc	(revision 191434)
+++ include/ext/random.tcc	(working copy)
@@ -848,6 +848,70 @@ 
       return __is;
     }
 
+
+  template<typename _RealType>
+    template<typename _OutputIterator,
+	     typename _UniformRandomNumberGenerator>
+      void
+      pareto_distribution<_RealType>::
+      __generate_impl(_OutputIterator __f, _OutputIterator __t,
+		      _UniformRandomNumberGenerator& __urng,
+		      const param_type& __p)
+      {
+	__glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator>)
+
+	result_type __mu = __p.mu();
+	result_type __malphinv = -result_type(1) / __p.alpha();
+	while (__f != __t)
+	  *__f++ = __mu * std::pow(this->_M_ud(__urng), __malphinv);
+      }
+
+  template<typename _RealType, typename _CharT, typename _Traits>
+    std::basic_ostream<_CharT, _Traits>&
+    operator<<(std::basic_ostream<_CharT, _Traits>& __os,
+	       const pareto_distribution<_RealType>& __x)
+    {
+      typedef std::basic_ostream<_CharT, _Traits>  __ostream_type;
+      typedef typename __ostream_type::ios_base    __ios_base;
+
+      const typename __ios_base::fmtflags __flags = __os.flags();
+      const _CharT __fill = __os.fill();
+      const std::streamsize __precision = __os.precision();
+      const _CharT __space = __os.widen(' ');
+      __os.flags(__ios_base::scientific | __ios_base::left);
+      __os.fill(__space);
+      __os.precision(std::numeric_limits<_RealType>::max_digits10);
+
+      __os << __x.alpha() << __space << __x.mu();
+      __os << __space << __x._M_ud;
+
+      __os.flags(__flags);
+      __os.fill(__fill);
+      __os.precision(__precision);
+      return __os;
+    }
+
+  template<typename _RealType, typename _CharT, typename _Traits>
+    std::basic_istream<_CharT, _Traits>&
+    operator>>(std::basic_istream<_CharT, _Traits>& __is,
+	       pareto_distribution<_RealType>& __x)
+    {
+      typedef std::basic_istream<_CharT, _Traits>  __istream_type;
+      typedef typename __istream_type::ios_base    __ios_base;
+
+      const typename __ios_base::fmtflags __flags = __is.flags();
+      __is.flags(__ios_base::dec | __ios_base::skipws);
+
+      _RealType __alpha, __mu;
+      __is >> __alpha >> __mu;
+      __is >> __x._M_ud;
+      __x.param(typename pareto_distribution<_RealType>::
+		param_type(__alpha, __mu));
+
+      __is.flags(__flags);
+      return __is;
+    }
+
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace
 
Index: testsuite/ext/random/pareto_distribution/operators/inequal.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/operators/inequal.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/operators/inequal.cc	(revision 0)
@@ -0,0 +1,44 @@ 
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// 2012-09-21  Edward M. Smith-Rowland  <3dw4rd@verizon.net>
+//
+// Copyright (C) 2012 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// 26.5.8.4.5 Class template pareto_distribution [rand.dist.ext.pareto]
+
+#include <ext/random>
+#include <testsuite_hooks.h>
+
+void
+test01()
+{
+  bool test __attribute__((unused)) = true;
+
+  __gnu_cxx::pareto_distribution<double> u(2.0, 3.0), v, w;
+
+  VERIFY( u != v );
+  VERIFY( !(v != w) );
+}
+
+int
+main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/ext/random/pareto_distribution/operators/equal.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/operators/equal.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/operators/equal.cc	(revision 0)
@@ -0,0 +1,44 @@ 
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// 2012-09-21  Edward M. Smith-Rowland  <3dw4rd@verizon.net>
+//
+// Copyright (C) 2012 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// 26.5.8.4.5 Class template pareto_distribution [rand.dist.ext.pareto]
+
+#include <ext/random>
+#include <testsuite_hooks.h>
+
+void
+test01()
+{
+  bool test __attribute__((unused)) = true;
+
+  __gnu_cxx::pareto_distribution<double> u(2.0, 3.0), v, w;
+
+  VERIFY( v == w );
+  VERIFY( !(u == v) );
+}
+
+int
+main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/ext/random/pareto_distribution/operators/serialize.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/operators/serialize.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/operators/serialize.cc	(revision 0)
@@ -0,0 +1,51 @@ 
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// 2012-09-21  Edward M. Smith-Rowland  <3dw4rd@verizon.net>
+//
+// Copyright (C) 2012 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// 26.4.8.3.* Class template pareto_distribution [rand.dist.ext.pareto]
+// 26.4.2.4 Concept RandomNumberDistribution [rand.concept.dist]
+
+#include <ext/random>
+#include <sstream>
+#include <testsuite_hooks.h>
+
+void
+test01()
+{
+  bool test __attribute__((unused)) = true;
+
+  std::stringstream str;
+  __gnu_cxx::pareto_distribution<double> u(1.5, 3.0), v;
+  std::minstd_rand0 rng;
+
+  u(rng); // advance
+  str << u;
+
+  str >> v;
+  VERIFY( u == v );
+}
+
+int
+main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/ext/random/pareto_distribution/cons/parms.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/cons/parms.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/cons/parms.cc	(revision 0)
@@ -0,0 +1,47 @@ 
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// 2012-09-21  Edward M. Smith-Rowland <3dw4rd@verizon.net>
+//
+// Copyright (C) 2012 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// 26.4.8.3.* Class template pareto_distribution [rand.dist.ext.pareto]
+// 26.4.2.4 Concept RandomNumberDistribution [rand.concept.dist]
+
+#include <ext/random>
+#include <testsuite_hooks.h>
+
+void
+test01()
+{
+  bool test __attribute__((unused)) = true;
+
+  __gnu_cxx::pareto_distribution<> u(1.5, 3.0);
+  VERIFY( u.alpha() == 1.5 );
+  VERIFY( u.mu() == 3.0 );
+  VERIFY( u.min() == 3.0 );
+  typedef __gnu_cxx::pareto_distribution<>::result_type result_type;
+  VERIFY( u.max() == std::numeric_limits<result_type>::max() );
+}
+
+int
+main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/ext/random/pareto_distribution/cons/default.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/cons/default.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/cons/default.cc	(revision 0)
@@ -0,0 +1,47 @@ 
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// 2012-09-21  Edward M. Smith-Rowland <3dw4rd@verizon.net>
+//
+// Copyright (C) 2012 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// 26.4.8.3.* Class template pareto_distribution [rand.dist.ext.pareto]
+// 26.4.2.4 Concept RandomNumberDistribution [rand.concept.dist]
+
+#include <ext/random>
+#include <testsuite_hooks.h>
+
+void
+test01()
+{
+  bool test __attribute__((unused)) = true;
+
+  __gnu_cxx::pareto_distribution<> u;
+  VERIFY( u.alpha() == 1.0 );
+  VERIFY( u.mu() == 1.0 );
+  VERIFY( u.min() == 1.0 );
+  typedef __gnu_cxx::pareto_distribution<>::result_type result_type;
+  VERIFY( u.max() == std::numeric_limits<result_type>::max() );
+}
+
+int
+main()
+{
+  test01();
+  return 0;
+}
Index: testsuite/ext/random/pareto_distribution/requirements/explicit_instantiation/1.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/requirements/explicit_instantiation/1.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/requirements/explicit_instantiation/1.cc	(revision 0)
@@ -0,0 +1,26 @@ 
+// { dg-do compile }
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// Copyright (C) 2012 Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+#include <ext/random>
+
+template class __gnu_cxx::pareto_distribution<float>;
+template class __gnu_cxx::pareto_distribution<double>;
+template class __gnu_cxx::pareto_distribution<long double>;
Index: testsuite/ext/random/pareto_distribution/requirements/typedefs.cc
===================================================================
--- testsuite/ext/random/pareto_distribution/requirements/typedefs.cc	(revision 0)
+++ testsuite/ext/random/pareto_distribution/requirements/typedefs.cc	(revision 0)
@@ -0,0 +1,36 @@ 
+// { dg-do compile }
+// { dg-options "-std=c++11" }
+// { dg-require-cstdint "" }
+//
+// 2012-09-21  Edward M. Smith-Rowland <3dw4rd@verizon.net>
+//
+// Copyright (C) 2012 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+//
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// 26.4.8.3.* Class template pareto_distribution [rand.dist.ext.pareto]
+// 26.4.2.4 Concept RandomNumberDistribution [rand.concept.dist]
+
+#include <ext/random>
+
+void
+test01()
+{
+  typedef __gnu_cxx::pareto_distribution<double> test_type;
+
+  typedef test_type::result_type result_type;
+  typedef test_type::param_type param_type;
+}