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dnorm.cpp File Reference

Normal density functions. More...

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

Go to the source code of this file.

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:
xa differentiable variable
muthe mean
stda 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 73 of file dnorm.cpp.

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

Definition at line 88 of file dnorm.cpp.

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

Definition at line 103 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:
xvariable vector of observations
mua double mean
stda double standard deviation
Returns:
returns the sum of negative loglikelihoods of the normal distribution
See also:

Definition at line 128 of file dnorm.cpp.

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

Definition at line 146 of file dnorm.cpp.

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

Definition at line 165 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:
xa vector of observations
mua variable mean
stda variable standard deviation
Returns:
returns the sum of negative loglikelihoods of the normal distribution
See also:

Definition at line 193 of file dnorm.cpp.

dvariable dnorm ( const dvar_vector residual,
const prevariable std 
)
Author:
Steven James Dean Martell
Date:
2011-06-21
Parameters:
residuala variable vector of residuals
stda variable standard deviation
Returns:
returns the sum of negative loglikelihoods of the normal distribution
See also:

Definition at line 257 of file dnorm.cpp.

dvariable dnorm ( const dvar_vector residual,
const double &  std 
)
Author:
Steven James Dean Martell
Date:
2011-06-21
Parameters:
residuala variable vector of residuals
stda double standard deviation
Returns:
returns the sum of negative loglikelihoods of the normal distribution
See also:

Definition at line 283 of file dnorm.cpp.

dvariable dnorm ( const dvar_vector residual,
const dvector std 
)
Author:
Steven James Dean Martell
Date:
2011-06-21
Parameters:
residuala variable vector of residuals
stda vector of standard deviations
Returns:
returns the sum of negative loglikelihoods of the normal distribution
See also:

Definition at line 309 of file dnorm.cpp.

dvariable dnorm ( const dvar_vector residual)
Author:
Steven James Dean Martell
Date:
2011-06-21
Parameters:
residuala variable vector of residuals
Returns:
returns the concentrated likelihood for the normal distribution.
See also:

Definition at line 343 of file dnorm.cpp.

dvariable dnorm ( const dmatrix obs,
const dvar_matrix pred 
)
Author:
Steven James Dean Martell
Date:
2011-06-21
Parameters:
obsa matrix of observed values
preda variable matrix of predicted values
Returns:
returns the concentrated likelihood for the normal distribution.
See also:

Definition at line 361 of file dnorm.cpp.

dvariable dnorm ( const dvar_vector residual,
const dvar_vector  std 
)
Author:
Steven James Dean Martell
Date:
2011-06-21
Parameters:
residuala variable vector of residuals
stda variable vector of standard deviations
Returns:
returns the sum of negative loglikelihoods of the normal distribution
See also:

Definition at line 380 of file dnorm.cpp.