Normal density functions. More...

#include "statsLib.h"
#include <admodel.h>
#include <df1b2fun.h>
#include <adrndeff.h>

Functions
dvariable	dnorm (const prevariable &x, const double &mu, const double &std)
dvariable	dnorm (const prevariable &x, const double &mu, const double &std, bool bLog=true)
df1b2variable	dnorm (const df1b2variable &x, const df1b2variable &mu, const df1b2variable &std, bool bLog=true)
df1b2variable	dnorm (const df1b2variable &x, const double &mu, const double &std)
df1b2variable	dnorm (const df1b2variable &x, const double &mu, const double &std, bool bLog=true)
dvariable	dnorm (const dvar_vector &x, const double &mu, const double &std)
dvariable	dnorm (const dvar_vector &x, const double &mu, const double &std, bool bLog=true)
df1b2variable	dnorm (const df1b2vector &x, const double &mu, const double &std, bool bLog=true)
dvariable	dnorm (const dvector &x, const prevariable &mu, const prevariable &std)
dvariable	dnorm (const dvar_vector &residual, const prevariable &std)
dvariable	dnorm (const dvar_vector &residual, const double &std)
dvariable	dnorm (const dvar_vector &residual, const dvector &std)
dvariable	dnorm (const dvar_vector &residual)
dvariable	dnorm (const dmatrix &obs, const dvar_matrix &pred)
dvariable	dnorm (const dvar_vector &residual, const dvar_vector std)

Detailed Description

Normal density functions.

Author:: Steven Martell

Date:: 2/05/2011

This file contains the negative loglikelihood functions for the normal distribution and is implemented to be consistent with the statistical program R with log=TRUE. The function dnorm is overloaded to accomodate single variables and vectors.

There are also overloaded versions where the user can specify the likelihood (i.e., log=FALSE)

The function is implemented as the negative log of the normal density function:

$0.5\ln(2 \pi) + \ln(\sigma) + 0.5\frac{(x-\mu)^2}{\sigma^2}$

where $\mu$ is the mean and $\sigma$ is the standard deviation.

The concentrated likelihood is implemented as:

$0.5 n \ln(\sum_{i=1}^{n}\epsilon^2)$

where $\epsilon$ is a vector of residuals with an assumed mean 0.

Definition in file dnorm.cpp.

Function Documentation

dvariable dnorm	(	const prevariable &	x,
		const double &	mu,
		const double &	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

x	a differentiable variable
mu	the mean
std	a double precision standard deviation

Returns:: returns the negative loglikelihood of the normal distribution

See also:

Definition at line 46 of file dnorm.cpp.

dvariable dnorm	(	const prevariable &	x,
		const double &	mu,
		const double &	std,
		bool	bLog = `true`
	)

Definition at line 59 of file dnorm.cpp.

df1b2variable dnorm	(	const df1b2variable &	x,
		const df1b2variable &	mu,
		const df1b2variable &	std,
		bool	bLog = `true`
	)

Definition at line 75 of file dnorm.cpp.

df1b2variable dnorm	(	const df1b2variable &	x,
		const double &	mu,
		const double &	std
	)

Definition at line 90 of file dnorm.cpp.

df1b2variable dnorm	(	const df1b2variable &	x,
		const double &	mu,
		const double &	std,
		bool	bLog = `true`
	)

Definition at line 105 of file dnorm.cpp.

dvariable dnorm	(	const dvar_vector &	x,
		const double &	mu,
		const double &	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

x	variable vector of observations
mu	a double mean
std	a double standard deviation

Returns:: returns the sum of negative loglikelihoods of the normal distribution

See also:

Definition at line 130 of file dnorm.cpp.

dvariable dnorm	(	const dvar_vector &	x,
		const double &	mu,
		const double &	std,
		bool	bLog = `true`
	)

Definition at line 148 of file dnorm.cpp.

df1b2variable dnorm	(	const df1b2vector &	x,
		const double &	mu,
		const double &	std,
		bool	bLog = `true`
	)

Definition at line 167 of file dnorm.cpp.

dvariable dnorm	(	const dvector &	x,
		const prevariable &	mu,
		const prevariable &	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

x	a vector of observations
mu	a variable mean
std	a variable standard deviation

Returns:: returns the sum of negative loglikelihoods of the normal distribution

See also:

Definition at line 195 of file dnorm.cpp.

dvariable dnorm	(	const dvar_vector &	residual,
		const prevariable &	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

residual	a variable vector of residuals
std	a variable standard deviation

Returns:: returns the sum of negative loglikelihoods of the normal distribution

See also:

Definition at line 259 of file dnorm.cpp.

dvariable dnorm	(	const dvar_vector &	residual,
		const double &	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

residual	a variable vector of residuals
std	a double standard deviation

Returns:: returns the sum of negative loglikelihoods of the normal distribution

See also:

Definition at line 285 of file dnorm.cpp.

dvariable dnorm	(	const dvar_vector &	residual,
		const dvector &	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

residual	a variable vector of residuals
std	a vector of standard deviations

Returns:: returns the sum of negative loglikelihoods of the normal distribution

See also:

Definition at line 311 of file dnorm.cpp.

dvariable dnorm ( const dvar_vector & residual )

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

residual a variable vector of residuals

Returns:: returns the concentrated likelihood for the normal distribution.

See also:

Definition at line 345 of file dnorm.cpp.

dvariable dnorm	(	const dmatrix &	obs,
		const dvar_matrix &	pred
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

obs	a matrix of observed values
pred	a variable matrix of predicted values

Returns:: returns the concentrated likelihood for the normal distribution.

See also:

Definition at line 363 of file dnorm.cpp.

dvariable dnorm	(	const dvar_vector &	residual,
		const dvar_vector	std
	)

Author:: Steven James Dean Martell

Date:: 2011-06-21

Parameters:

residual	a variable vector of residuals
std	a variable vector of standard deviations

Returns:: returns the sum of negative loglikelihoods of the normal distribution

See also:

Definition at line 382 of file dnorm.cpp.

Functions

Detailed Description

Function Documentation