//*******************************************************************************
//?Repast?.NET?was?made?possible?in?part?by?the?Defense?Program?Office?for?Mission?
//?Assurance?Naval?Surface?Warfare?Center?Dahlgren?Virginia.
//?For?all?questions?please?send?e-mail?to?repast-interest@sourceforge.net.
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/*
based?on?code?under?the?following?license:
Copyright??1999?CERN?-?European?Organization?for?Nuclear?Research.
Permission?to?use?copy?modify?distribute?and?sell?this?software?and?its?documentation?for?any?purpose?
is?hereby?granted?without?fee?provided?that?the?above?copyright?notice?appear?in?all?copies?and?
that?both?that?copyright?notice?and?this?permission?notice?appear?in?supporting?documentation.?
CERN?makes?no?representations?about?the?suitability?of?this?software?for?any?purpose.?
It?is?provided?“as?is“?without?expressed?or?implied?warranty.*/
using?System;
using?Probability?=?cern.jet.stat.Probability;
using?RandomStartingValueSource?=?cern.jet.random.engine.RandomStartingValueSource;
namespace?cern.jet.random
{
	///?
Normal?（aka?Gaussian）?distribution;?See?the??math?definition
	///?and??animated?definition.
	///?
???????????????????????
	///?1???????????????????????2
	///?pdf（x）?=?---------????exp（?-?（x-mean）?/?2v?）?
	///?sqrt（2pi*v）
	///?x
	///?-
	///?1????????|?|?????????????????2
	///?cdf（x）?=?---------????|????exp（?-?（t-mean）?/?2v?）?dt
	///?sqrt（2pi*v）|?|
	///?-
	///?-inf.
	///?

	///?where?v?=?variance?=?standardDeviation^2.
	///?

	///?Instance?methods?operate?on?a?user?supplied?uniform?random?number?generator;?they?are?unsynchronized.
	///?

	///?Static?methods?operate?on?a?default?uniform?random?number?generator;?they?are?synchronized.
	///?

	///?Implementation:?Polar?Box-Muller?transformation.?See?
	///?G.E.P.?Box?M.E.?Muller?（1958）:?A?note?on?the?generation?of?random?normal?deviates?Annals?Math.?Statist.?29?610-611.
	///?

	///?

	///???wolfgang.hoschek@cern.ch
	///?
	///???1.0?09/24/99
	///?
	public?class?Normal:AbstractContinousDistribution
	{
		protected?internal?double?mean;
		protected?internal?double?variance;
		protected?internal?double?standardDeviation;
		
		protected?internal?double?cache;?//?cache?for?Box-Mueller?algorithm?
		protected?internal?bool?cacheFilled;?//?Box-Mueller
		
		protected?internal?double?SQRT_INV;?//?performance?cache
		
		//?The?uniform?random?number?generated?shared?by?all?static?methods.
		protected?internal?static?Normal?shared;
		///?
?Constructs?a?normal?（gauss）?distribution.
		///?Example: