[Boost-commit] svn:boost r38455 - sandbox/math_toolkit/libs/math/doc/distributions

From: john_at_[hidden]
Date: 2007-08-05 13:52:52

Author: johnmaddock
Date: 2007-08-05 13:52:48 EDT (Sun, 05 Aug 2007)
New Revision: 38455
URL: http://svn.boost.org/trac/boost/changeset/38455

Log:
Fix filename Case.
Added:
   sandbox/math_toolkit/libs/math/doc/distributions/rayleigh.qbk
      - copied unchanged from r38454, /sandbox/math_toolkit/libs/math/doc/distributions/Rayleigh.qbk
Removed:
   sandbox/math_toolkit/libs/math/doc/distributions/Rayleigh.qbk

Deleted: sandbox/math_toolkit/libs/math/doc/distributions/Rayleigh.qbk
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/distributions/Rayleigh.qbk	2007-08-05 13:52:48 EDT (Sun, 05 Aug 2007)
+++ (empty file)
@@ -1,110 +0,0 @@
-[section:rayleigh Rayleigh Distribution]
-
-
-``#include <boost/math/distributions/rayleigh.hpp>``
-
-   namespace boost{ namespace math{ 
-      
-   template <class RealType = double, 
-             class ``__Policy``   = ``__policy_class`` >
-   class rayleigh_distribution;
-   
-   typedef rayleigh_distribution<> rayleigh;
-   
-   template <class RealType, class ``__Policy``>
-   class rayleigh_distribution
-   {
-   public:
-      typedef RealType value_type;
-      typedef Policy   policy_type;
-      // Construct:
-      rayleigh_distribution(RealType sigma = 1)
-      // Accessors:
-      RealType sigma()const;
-   };
-   
-   }} // namespaces
-   
-The [@http://en.wikipedia.org/wiki/Rayleigh_distribution Rayleigh distribution]
-is a continuous distribution with the 
-[@http://en.wikipedia.org/wiki/Probability_density_function probability density function]:
-
-f(x; sigma) = x * exp(-x[super 2]/2 [sigma][super 2]) / [sigma][super 2]
-
-For sigma parameter [sigma][space] > 0, and x > 0.
-
-The Rayleigh distribution is often used where two orthogonal components
-have an absolute value,
-for example, wind velocity and direction may be combined to yield a wind speed,
-or real and imaginary components may have absolute values that are Rayleigh distributed.
-
-The following graph illustrates how the Probability density Function(pdf) varies with the shape parameter [sigma]:
-[$../graphs/rayleigh_pdf.png]
-
-and the Cumulative Distribution Function (cdf)
-[$../graphs/rayleigh_cdf.png]
-
-[h4 Related distributions]
-
-The absolute value of two independent normal distributions X and Y, [radic] (X[super 2] + Y[super 2])
-is a Rayleigh distribution.
-
-The [@http://en.wikipedia.org/wiki/Chi_distribution Chi],
-[@http://en.wikipedia.org/wiki/Rice_distribution Rice]
-and [@http://en.wikipedia.org/wiki/Weibull_distribution Weibull] distributions are generalizations of the
-[@http://en.wikipedia.org/wiki/Rayleigh_distribution Rayleigh distribution]. 
-
-[h4 Member Functions]
-
-   rayleigh_distribution(RealType sigma = 1);
-   
-Constructs a [@http://en.wikipedia.org/wiki/Rayleigh_distribution 
-Rayleigh distribution] with [sigma] /sigma/.
-
-Requires that the [sigma] parameter is greater than zero, 
-otherwise calls __domain_error.
-
-   RealType sigma()const;
-   
-Returns the /sigma/ 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 domain of the random variable is \[0, max_value\].
-
-[h4 Accuracy]
-
-The Rayleigh distribution is implemented in terms of the 
-standard library `sqrt` and `exp` and as such should have very low error rates.
-Some constants such as skewness and kurtosis were calculated using
-NTL RR type with 150-bit accuracy, about 50 decimal digits.
-
-[h4 Implementation]
-
-In the following table [sigma][space] is the sigma parameter of the distribution, 
-/x/ is the random variate, /p/ is the probability and /q = 1-p/.
-
-[table
-[[Function][Implementation Notes]]
-[[pdf][Using the relation: pdf = x * exp(-x[super 2])/2 [sigma][super 2] ]]
-[[cdf][Using the relation: p = 1 - exp(-x[super 2]/2) [sigma][super 2][space] = -__expm1(-x[super 2]/2) [sigma][super 2]]]
-[[cdf complement][Using the relation: q =  exp(-x[super 2]/ 2) * [sigma][super 2] ]]
-[[quantile][Using the relation: x = sqrt(-2 * [sigma] [super 2]) * log(1 - p)) = sqrt(-2 * [sigma] [super 2]) * __log1p(-p))]]
-[[quantile from the complement][Using the relation: x = sqrt(-2 * [sigma] [super 2]) * log(q)) ]]
-[[mean][[sigma] * sqrt([pi]/2) ]]
-[[variance][[sigma][super 2] * (4 - [pi]/2) ]]
-[[mode][[sigma] ]]
-[[skewness][Constant from [@http://mathworld.wolfram.com/RayleighDistribution.html Weisstein, Eric W. "Weibull Distribution." From MathWorld--A Wolfram Web Resource.] ]]
-[[kurtosis][Constant from [@http://mathworld.wolfram.com/RayleighDistribution.html Weisstein, Eric W. "Weibull Distribution." From MathWorld--A Wolfram Web Resource.] ]]
-[[kurtosis excess][Constant from [@http://mathworld.wolfram.com/RayleighDistribution.html Weisstein, Eric W. "Weibull Distribution." From MathWorld--A Wolfram Web Resource.] ]]
-]
-
-[h4 References]
-* [@http://en.wikipedia.org/wiki/Rayleigh_distribution ]
-* [@http://mathworld.wolfram.com/RayleighDistribution.html Weisstein, Eric W. "Rayleigh Distribution." From MathWorld--A Wolfram Web Resource.]
-
-[endsect][/section:Rayleigh Rayleigh]
-