[Boost-commit] svn:boost r38454 - sandbox/math_toolkit/libs/math/doc/distributions

From: john_at_[hidden]
Date: 2007-08-05 13:50:09

Author: johnmaddock
Date: 2007-08-05 13:50:01 EDT (Sun, 05 Aug 2007)
New Revision: 38454
URL: http://svn.boost.org/trac/boost/changeset/38454

Log:
Fix filename case
Added:
   sandbox/math_toolkit/libs/math/doc/distributions/pareto.qbk
      - copied unchanged from r38453, /sandbox/math_toolkit/libs/math/doc/distributions/Pareto.qbk
Removed:
   sandbox/math_toolkit/libs/math/doc/distributions/Pareto.qbk

Deleted: sandbox/math_toolkit/libs/math/doc/distributions/Pareto.qbk
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/distributions/Pareto.qbk	2007-08-05 13:50:01 EDT (Sun, 05 Aug 2007)
+++ (empty file)
@@ -1,107 +0,0 @@
-[section:pareto Pareto Distribution]
-
-
-``#include <boost/math/distributions/pareto.hpp>``
-
-   namespace boost{ namespace math{ 
-      
-   template <class RealType = double, 
-             class ``__Policy``   = ``__policy_class`` >
-   class pareto_distribution;
-   
-   typedef pareto_distribution<> pareto;
-   
-   template <class RealType, class ``__Policy``>
-   class pareto_distribution
-   {
-   public:
-      typedef RealType value_type;
-      // Constructor:
-      pareto_distribution(RealType location = 1, RealType shape = 1)
-      // Accessors:
-      RealType location()const;
-      RealType shape()const;
-   };
-   
-   }} // namespaces
-   
-The [@http://en.wikipedia.org/wiki/pareto_distribution Pareto distribution]
-is a continuous distribution with the 
-[@http://en.wikipedia.org/wiki/Probability_density_function probability density function (pdf)]:
-
-f(x; [alpha], [beta]) = [alpha][beta][super [alpha]] / x[super [alpha]+ 1]
-
-For shape parameter [alpha][space] > 0, and location parameter [beta][space] > 0, and [alpha][space] > 0.
-
-The [@http://mathworld.wolfram.com/paretoDistribution.html Pareto distribution]
-often describes the larger compared to the smaller.
-A classic example is that 80% of the wealth is owned by 20% of the population.
-
-The following graph illustrates how the PDF varies with the shape parameter [alpha]:
-
-[/$../graphs/paretoShape.png]
-[/ TODO produce a graph as png or svg]
-[@http://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Pareto_distributionPDF.png/325px-Pareto_distributionPDF.png Pareto pdf]
-
-[h4 Related distributions]
-
-  
-[h4 Member Functions]
-
-   pareto_distribution(RealType location = 1, RealType shape = 1);
-   
-Constructs a [@http://en.wikipedia.org/wiki/pareto_distribution 
-pareto distribution] with shape /shape/ and scale /scale/.
-
-Requires that the /shape/ and /scale/ parameters are both greater than zero, 
-otherwise calls __domain_error.
-   
-   RealType location()const;
-      
-Returns the /location/ parameter of this distribution.
-
-   RealType shape()const;
-   
-Returns the /shape/ parameter of this distribution.
-
-[h4 Non-member Accessors]
-
-All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
-distributions are supported: __usual_accessors.
-
-The supported domain of the random variable is \[location, [infin]\].
-
-[h4 Accuracy]
-
-The pareto distribution is implemented in terms of the 
-standard library `exp` functions plus __expm1
-and as such should have very low error rates
-except when probability is very close to unity.
-
-[h4 Implementation]
-
-In the following table [alpha][space] is the shape parameter of the distribution, and
-[beta][space] is its location parameter, /x/ is the random variate, /p/ is the probability
-and its complement /q = 1-p/.
-
-[table
-[[Function][Implementation Notes]]
-[[pdf][Using the relation: pdf p = [alpha][beta][super [alpha]]/x[super [alpha] +1] ]]
-[[cdf][Using the relation: cdf p = 1 - ([beta][space] / x)[super [alpha]] ]]
-[[cdf complement][Using the relation: q = 1 - p = -([beta][space] / x)[super [alpha]] ]]
-[[quantile][Using the relation: x = [alpha] / (1 - p)[super 1/[beta]] ]]
-[[quantile from the complement][Using the relation: x =  [alpha] / (q)[super 1/[beta]] ]]
-[[mean][[alpha][beta] / ([beta] - 1) ]]
-[[variance][[beta][alpha][super 2] / ([beta] - 1)[super 2] ([beta] - 2) ]]
-[[mode][[alpha]]]
-[[skewness][Refer to [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
-[[kurtosis][Refer to [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
-[[kurtosis excess][Refer to [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
-]
-
-[h4 References]
-* [@http://en.wikipedia.org/wiki/pareto_distribution Pareto Distribution]
-* [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.]
-
-[endsect][/section:pareto pareto]
-