Functions
double	cumd_norm (const double &x)
	Culative normal distribution; constant objects. More...

prevariable &	cumd_norm (const prevariable &_x)
	Culative normal distribution; variable objects. More...

double	density_negbinomial (double x, double mu, double tau)
	Negative bionomial density; constant objects. More...

double	gamma_density (double x, double r, double mu)
	Gamma probability density function; constant objects. More...

dvariable	gamma_density (const prevariable &_x, double r, double mu)
	Gamma probability density function; variable objects. More...

dvariable	gamma_density (const dvariable &_x, const dvariable &_r, const dvariable &_mu)
	Gamma probability density function; variable objects. More...

double	log_density_negbinomial (double x, double mu, double tau)
	Log negative bionomial density; constant objects. More...

double	log_density_poisson (double x, double mu)
	Log Poisson density; constant objects. More...

df1b2variable	log_density_poisson (double x, const df1b2variable &mu)
	Log Poisson density; random effects objects. More...

dvariable	log_density_poisson (double x, const prevariable &mu)
	Log Poisson density; variable objects. More...

dvariable	log_gamma_density (const prevariable &_x, double r, double mu)
	file More...

dvariable	log_gamma_density (const dvariable &_x, const dvariable &_r, const dvariable &_mu)
	Log gamma probability density function; variable objects. More...

double	log_gamma_density (double x, double r, double mu)
	Log gamma probability density function; constant objects. More...

dvariable	log_negbinomial_density (double x, const prevariable &mu, const prevariable &tau)
	Log negative bionomial density; variable objects. More...

dvariable	negbinomial_density (double x, const prevariable &mu, const prevariable &tau)
	Negative bionomial density; variable objects. More...

df1b2variable	negbinomial_density (double x, const df1b2variable &mu, const df1b2variable &tau)
	Log negative bionomial density; random effects objects. More...

Detailed Description

Function Documentation

double cumd_norm ( const double & x )

Culative normal distribution; constant objects.

Parameters

x	Normalized "Z" score (subtact the mean and divide by the stdard deviation).

Returns: Probablity that of an observation will exceed the argument.

Definition at line 90 of file cumdist.cpp.

Referenced by ageLengthKey(), ALK(), beta_deviate(), bounded_multivariate_normal(), bounded_multivariate_normal_mcmc(), bounded_robust_multivariate_normal(), cumd_mixture(), cumd_mixture_02(), cumd_norm_logistic(), cumd_normal_logistic_mixture(), cumd_normal_mixture(), gamma_deviate(), get_bounded_normal(), get_bounded_normal_virtual(), ghk(), ghk_choleski(), ghk_choleski_m(), ghk_m(), inv_cumd_norm(), new_probing_bounded_multivariate_normal(), new_probing_bounded_multivariate_normal_mcmc(), probing_bounded_multivariate_normal(), probing_bounded_multivariate_normal_mcmc(), robust_normal_logistic_mixture_deviate(), robust_normal_mixture_deviate(), and t_deviate().

prevariable& cumd_norm ( const prevariable & _x )

Culative normal distribution; variable objects.

Parameters

_x	Normalized "Z" score (subtact the mean and divide by the stdard deviation).

Returns: Probablity that of an observation will exceed the argument.

Definition at line 184 of file vcumdist.cpp.

double density_negbinomial	(	double	x,
		double	mu,
		double	tau
	)

Negative bionomial density; constant objects.

A local parameter r is used to make it robust. $r=\frac{\mu}{10.0^{-120}+\tau-1.0}$

Parameters

x
mu
tau

Returns: NegativeBinomial density. $\frac{\Gamma(x+r)}{\Gamma(r)x!}(\frac{r}{r+\mu})^r(\frac{\mu}{r+\mu})^x$

Definition at line 43 of file cnegbin.cpp.

double gamma_density	(	double	x,
		double	r,
		double	mu
	)

Gamma probability density function; constant objects.

Mean $= \frac{r}{\mu}$ .

Parameters

x	Argument, $x \ge 0$ .
r	Shape parameter, .
mu	Slope parameter, $\mu > 0$ .

Returns: $\frac{\mu^r}{\Gamma(r)}x^{r-1}e^{-\mu x}$

Definition at line 21 of file cgamdens.cpp.

dvariable gamma_density	(	const prevariable &	_x,
		double	r,
		double	mu
	)

Gamma probability density function; variable objects.

Mean $= \frac{r}{\mu}$ .

Parameters

_x	Differentiable argument, $x \ge 0$ .
r	Constant shape parameter, .
mu	Constang slope parameter, $\mu > 0$ .

Returns: Dvariable containing $\frac{\mu^r}{\Gamma(r)}x^{r-1}e^{-\mu x}$

Definition at line 51 of file linad99/vgamdens.cpp.

dvariable gamma_density	(	const dvariable &	_x,
		const dvariable &	_r,
		const dvariable &	_mu
	)

Gamma probability density function; variable objects.

Parameters

_x	Differentiable argument, $x \ge 0$ .
_r	Differentiable, .
_mu	Differentiable, $\mu > 0$ .

Returns: Dvariable containing $\frac{\mu^r}{\Gamma(r)}x^{r-1}e^{-\mu x}$

Definition at line 65 of file linad99/vgamdens.cpp.

double log_density_negbinomial	(	double	x,
		double	mu,
		double	tau
	)

Log negative bionomial density; constant objects.

A local parameter r is used to make it robust. $r=\frac{\mu}{10.0^{-120}+\tau-1.0}$

Parameters

x
mu
tau

Returns: Log of NegativeBinomial density. $log(\Gamma(x+r))-log(\Gamma(r))-log(x!)+rlog(r)+xlog(\mu)-(r+x)log(r+\mu)$

Definition at line 22 of file cnegbin.cpp.

Referenced by nllNegativeBinomial2().

double log_density_poisson	(	double	x,
		double	mu
	)

Log Poisson density; constant objects.

Parameters

x	Number of observed occurences, .
mu	Mean or expected value, $\mu$ .

Returns: Log of Poisson density. $-\mu+k*\log(\mu)-k!$ .

Definition at line 61 of file cnegbin.cpp.

df1b2variable log_density_poisson	(	double	x,
		const df1b2variable &	mu
	)

Log Poisson density; random effects objects.

Parameters

x	Number of observed occurences, .
mu	Mean or expected value, $\mu$ .

Returns: Log of Poisson density. $-\mu+k*\log(\mu)-k!$ .

Definition at line 73 of file df1b2negb.cpp.

dvariable log_density_poisson	(	double	x,
		const prevariable &	mu
	)

Log Poisson density; variable objects.

Parameters

x	Number of observed occurences, .
mu	Mean or expected value, $\mu$ .

Returns: Log of Poisson density. $-\mu+k*\log(\mu)-k!$ .

Definition at line 81 of file vnegbin.cpp.

dvariable log_gamma_density	(	const prevariable &	_x,
		double	r,
		double	mu
	)

file

Author: David Fournier

Copyright: Copyright (c) 2008-2020 Regents of the University of California

Functions for gamma probability density; differentiable (variable) objects.

Log gamma probability density function; variable objects.

Parameters

_x	dvariable argument
r	double argument
mu	double argument

Returns: $r\log{\mu} + (r-1)*\log{x}-\mu*x-\log{\Gamma(r)}$

Definition at line 18 of file linad99/vgamdens.cpp.

dvariable log_gamma_density	(	const dvariable &	_x,
		const dvariable &	_r,
		const dvariable &	_mu
	)

Log gamma probability density function; variable objects.

Parameters

_x	dvariable argument
_r	dvariable argument
_mu	dvariable argument

Returns: $r\log{\mu} + (r-1)*\log{x}-\mu*x-\log{\Gamma(r)}$

Definition at line 33 of file linad99/vgamdens.cpp.

double log_gamma_density	(	double	x,
		double	r,
		double	mu
	)

Log gamma probability density function; constant objects.

Mean $= \frac{r}{\mu}$ .

Parameters

x	Argument, $x \ge 0$ .
r	Shape parameter, .
mu	Slope parameter, $\mu > 0$ .

Returns: $r\log{\mu} + (r-1)\log{x}-\mu x-\log{\Gamma(r)}$

Definition at line 35 of file cgamdens.cpp.

Referenced by nllGamma().

dvariable log_negbinomial_density	(	double	x,
		const prevariable &	mu,
		const prevariable &	tau
	)

Log negative bionomial density; variable objects.

A local parameter r is used to make it robust. $r=\frac{\mu}{10.0^{-120}+\tau-1.0}$

Parameters

x
mu
tau

Returns: Log of NegativeBinomial density. $log(\Gamma(x+r))-log(\Gamma(r))-log(x!)+rlog(r)+xlog(\mu)-(r+x)log(r+\mu)$

Definition at line 21 of file vnegbin.cpp.

dvariable negbinomial_density	(	double	x,
		const prevariable &	mu,
		const prevariable &	tau
	)

Negative bionomial density; variable objects.

A local parameter r is used to make it robust. $r=\frac{\mu}{10.0^{-120}+\tau-1.0}$

Parameters

x
mu
tau

Returns: Log of NegativeBinomial density. $\frac{\Gamma(x+r)}{\Gamma(r)x!}(\frac{r}{r+\mu})^r(\frac{\mu}{r+\mu})^x$

Definition at line 49 of file vnegbin.cpp.

df1b2variable negbinomial_density	(	double	x,
		const df1b2variable &	mu,
		const df1b2variable &	tau
	)

Log negative bionomial density; random effects objects.

A local parameter r is used to make it robust. $r=\frac{\mu}{\tau-1.0}$

Parameters

x
mu
tau

Returns: Log of NegativeBinomial density. $log(\Gamma(x+r))-log(\Gamma(r))-log(x!)+rlog(r)+xlog(\mu)-(r+x)log(r+\mu)$ Negative bionomial density; random effects objects. A local parameter r is used to make it robust. $r=\frac{\mu}{10.0^{-120}+\tau-1.0}$

Parameters

x
mu
tau

Returns: NegativeBinomial density. $\frac{\Gamma(x+r)}{\Gamma(r)x!}(\frac{r}{r+\mu})^r(\frac{\mu}{r+\mu})^x$

Definition at line 50 of file df1b2negb.cpp.