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48 lines
2.1 KiB
C++
48 lines
2.1 KiB
C++
// $Id: generalGammaDistributionLaguerre.h 2865 2007-11-27 11:00:26Z itaymay $
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// version 1.00
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// last modified Sep 2004
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#ifndef ___GENERAL_GAMMA_DIST_LAGUERRE
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#define ___GENERAL_GAMMA_DIST_LAGUERRE
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/************************************************************
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This class differ from the regular generalGammaDistribution in that
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the rateCategories and their probabilities are not constructed using Yang's quantile method.
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Instead the general Guass-Laguerre quadrature method is used.
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For example, if we want to compute the likelihood over the rate distribution,
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then we need to solve the integral
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I[0_to_infinity]{P(data|r)*P(r)}
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= I[0_to_infinity]{P(data|r)*b^a / Gamma(a)* exp(-b*r) * r^(a-1)dr} //a = alpha, b = beta
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= b^(a)/Gamma(a) * I[0_to_infinity]{P(data|m/b) * exp(-m) * (m/b)^(a')/bdm} ///substitute m=b*r, a'=a-1
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= 1/Gamma(a) * I[0_to_infinity]{P(data|m/b) * exp(-m) * m^a' dm} //
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Now - we can use the Guass-Laguerre formula, to get an approximation for the Integral.
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The Xj and Wj are the absicassas and weights of the Laguerre polynoms
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= 1/Gamma(a) * sum[j = 0_to_catNum]{P(data|Xj/b) * Wj}
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The rates are the Xj/b and their priors is Wj/Gamma(a)
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The quadrature method is explained in Numerical Recipes (Press et al.; chapter 4.5)
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and is also mentioned in Felsenstein 2001 (JME 53: 447-455).
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************************************************************/
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#include "definitions.h"
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#include "generalGammaDistribution.h"
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class generalGammaDistributionLaguerre : public generalGammaDistribution {
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public:
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explicit generalGammaDistributionLaguerre();
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explicit generalGammaDistributionLaguerre(MDOUBLE alpha, MDOUBLE beta, int in_number_of_categories);
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explicit generalGammaDistributionLaguerre(const generalGammaDistributionLaguerre& other);
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virtual ~generalGammaDistributionLaguerre();
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virtual void setGammaParameters(int numOfCategories ,MDOUBLE alpha, MDOUBLE beta);
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virtual distribution* clone() const { return new generalGammaDistributionLaguerre(*this); }
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virtual MDOUBLE getBorder(const int i) const;
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protected:
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virtual void fillRatesAndProbs(int catNum);
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};
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#endif
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