Beta density functions. More...

#include "statsLib.h"

Functions
dvariable	dbeta (const dvariable &x, const double &shape1, const double &shape2)
dvariable	dbeta (const dvariable &x, const dvariable &shape1, const dvariable &shape2)
dvariable	dbeta (const dvariable &x, const prevariable &shape1, const prevariable &shape2)

Detailed Description

Beta density functions.

This file contains the negative loglikelihood functions for the beta distribution. The function dbeta is overloaded to accomodate single variables and vectors.

Author:: Steven Martell

Date:: 2/27/2011

Remarks:: The general log density function is implemented as:
$-\ln(\Gamma(a+b)) +\ln(\Gamma(a)) + \ln(\Gamma(b))-(a-1)\ln(x)-(b-1)\ln(1-x)$
where and are the shape parameters and is the quantile value that must lie between 0-1.

Definition in file dbeta.cpp.

Function Documentation

dvariable dbeta	(	const dvariable &	x,
		const double &	shape1,
		const double &	shape2
	)

Author:: Steven Martell

Parameters:

shape1	= a parameter (a > 0)
shape2	= b parameter (b > 0)

Remarks:: x must greater than 0 and less than 1. The mean is given by a/(a+b) and the variance ab/((a+b)^2(a+b+1)).

The log density function is implemented as:

$-\ln(\Gamma(a+b)) +\ln(\Gamma(a)) + \ln(\Gamma(b))-(a-1)\ln(x)-(b-1)\ln(1-x)$

Definition at line 37 of file dbeta.cpp.

dvariable dbeta	(	const dvariable &	x,
		const dvariable &	shape1,
		const dvariable &	shape2
	)

Definition at line 58 of file dbeta.cpp.

dvariable dbeta	(	const dvariable &	x,
		const prevariable &	shape1,
		const prevariable &	shape2
	)

Definition at line 79 of file dbeta.cpp.

Functions

Detailed Description

Function Documentation