Probability Density Functions.

## Functions

double cumd_norm (const double &x)
Culative normal distribution; constant objects.
prevariablecumd_norm (const prevariable &_x)
Culative normal distribution; variable objects.
double density_negbinomial (double x, double mu, double tau)
Negative bionomial density; constant objects.
double gamma_density (double x, double r, double mu)
Gamma probability density function; constant objects.
dvariable gamma_density (const prevariable &_x, double r, double mu)
Gamma probability density function; variable objects.
dvariable gamma_density (const dvariable &_x, const dvariable &_r, const dvariable &_mu)
Gamma probability density function; variable objects.
double log_density_negbinomial (double x, double mu, double tau)
Log negative bionomial density; constant objects.
double log_density_poisson (double x, double mu)
Log Poisson density; constant objects.
df1b2variable log_density_poisson (double x, const df1b2variable &mu)
Log Poisson density; random effects objects.
dvariable log_density_poisson (double x, const prevariable &mu)
Log Poisson density; variable objects.
dvariable log_gamma_density (const prevariable &_x, double r, double mu)
Log gamma probability density function; variable objects.
dvariable log_gamma_density (const dvariable &_x, const dvariable &_r, const dvariable &_mu)
Log gamma probability density function; variable objects.
double log_gamma_density (double x, double r, double mu)
Log gamma probability density function; constant objects.
dvariable log_negbinomial_density (double x, const prevariable &mu, const prevariable &tau)
Log negative bionomial density; variable objects.
df1b2variable negbinomial_density (double x, const df1b2variable &mu, const df1b2variable &tau)
Log negative bionomial density; random effects objects.
dvariable negbinomial_density (double x, const prevariable &mu, const prevariable &tau)
Negative bionomial density; variable objects.

## 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.

 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 181 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.

Parameters:
 x mu tau
Returns:
NegativeBinomial density.

Definition at line 43 of file cnegbin.cpp.

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

Gamma probability density function; constant objects.

Mean .

Parameters:
 x Argument, . r Shape parameter, . mu Slope parameter, .
Returns:

Definition at line 24 of file cgamdens.cpp.

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

Gamma probability density function; variable objects.

Mean .

Parameters:
 _x Differentiable argument, . r Constant shape parameter, . mu Constang slope parameter, .
Returns:
Dvariable containing

Definition at line 54 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, . _r Differentiable, . _mu Differentiable, .
Returns:
Dvariable containing

Definition at line 68 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.

Parameters:
 x mu tau
Returns:
Log of NegativeBinomial density.

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, .
Returns:
Log of Poisson density. .

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, .
Returns:
Log of Poisson density. .

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, .
Returns:
Log of Poisson density. .

Definition at line 83 of file vnegbin.cpp.

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

Log gamma probability density function; variable objects.

Parameters:
 _x dvariable argument r double argument mu double argument
Returns:

Definition at line 21 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:

Definition at line 36 of file linad99/vgamdens.cpp.

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

Log gamma probability density function; constant objects.

Mean .

Parameters:
 x Argument, . r Shape parameter, . mu Slope parameter, .
Returns:

Definition at line 38 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.

Parameters:
 x mu tau
Returns:
Log of NegativeBinomial density.

Definition at line 25 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.

Parameters:
 x mu tau
Returns:
Log of NegativeBinomial density. Negative bionomial density; random effects objects. A local parameter r is used to make it robust.
Parameters:
 x mu tau
Returns:
NegativeBinomial density.

Definition at line 50 of file df1b2negb.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.

Parameters:
 x mu tau
Returns:
Log of NegativeBinomial density.

Definition at line 51 of file vnegbin.cpp.