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Functions
dgamma.cpp File Reference
Statistical Fuctions

(Last Changed on May 31, 2017 for git-revision 2eb364ddb56337e6fe5aa966ed3c7175e5eb2d03.)

Gamma density functions. More...

#include "statsLib.h"

Go to the source code of this file.

Functions

dvariable dgamma (const dvariable &x, const double &a, const double &b)
 
dvariable dgamma (const dvariable &x, const dvariable &a, const dvariable &b)
 
dvariable dgamma (const dvector &x, const prevariable &a, const prevariable &b)
 
dvariable dgamma (const dvector &x, const prevariable &a, const dvar_vector &b)
 
dvariable dgamma (const dvector &x, const dvar_vector &a, const dvar_vector &b)
 
dvariable dgamma (const dvector &x, const dvar_vector &a, const prevariable &b)
 

Detailed Description

Gamma density functions.

Author
Steven Martell and Mollie Brooks
Date
2/28/2011

This file contains the negative loglikelihood functions for the gamma distribution. The function dgamma is implemented as:

\[ -a \ln(b) + \ln(\Gamma(a)) - (a-1) \ln(x)+b x \]

The expected value is given by $ E(x)=a/b $ and the variance as $ V(x)=a/b^2 $. Note that you can also derive $a$ and $b$ from the expected value and variance via:

\[ a = \frac{E(x)^2}{V(x)}, \quad b=\sqrt{\frac{a}{V(x)}} \]

Definition in file dgamma.cpp.

Function Documentation

dvariable dgamma ( const dvariable &  x,
const double &  a,
const double &  b 
)
Date
2/28/2011
Author
Steven Martell
Parameters
xis the quantile and must be greater than 0.
ais the shape parameter and must be positive.
bis the rate parameter and must be positive.
Returns
a dvariable object
See Also

Definition at line 37 of file dgamma.cpp.

dvariable dgamma ( const dvariable &  x,
const dvariable &  a,
const dvariable &  b 
)
Date
2/28/2011
Author
Steven Martell
Parameters
xis the quantile and must be greater than 0.
ais the shape parameter and must be positive.
bis the rate parameter and must be positive.
Returns
a dvariable object
See Also

Definition at line 66 of file dgamma.cpp.

dvariable dgamma ( const dvector &  x,
const prevariable &  a,
const prevariable &  b 
)
Date
8/1/2011
Author
Mollie Brooks
Parameters
xis the quantile and must be greater than 0.
ais the shape parameter and must be positive.
bis the rate parameter and must be positive.
Returns
a dvariable object $ \Sigma_i (-a \ln(b)+\ln(\Gamma(a))-(a-1)\ln(x_i)+b x_i) $
See Also

Definition at line 97 of file dgamma.cpp.

dvariable dgamma ( const dvector &  x,
const prevariable &  a,
const dvar_vector &  b 
)
Date
8/1/2011
Author
Mollie Brooks
Parameters
xis the quantile and must be greater than 0.
ais the shape parameter and must be positive.
bis the rate parameter and must be positive.
Returns
a dvariable object $ \Sigma_i (-a \ln(b_i)+\ln(\Gamma(a))-(a-1)\ln(x_i)+b_i x_i) $
See Also

Definition at line 129 of file dgamma.cpp.

dvariable dgamma ( const dvector &  x,
const dvar_vector &  a,
const dvar_vector &  b 
)
Date
8/1/2011
Author
Mollie Brooks
Parameters
xis the quantile and must be greater than 0.
ais the shape parameter and must be positive.
bis the rate parameter and must be positive.
Returns
a dvariable object $ \Sigma_i (-a_i \ln(b_i)+\ln(\Gamma(a_i))-(a_i-1)\ln(x_i)+b_i x_i) $
See Also

Definition at line 163 of file dgamma.cpp.

dvariable dgamma ( const dvector &  x,
const dvar_vector &  a,
const prevariable &  b 
)
Date
8/1/2011
Author
Mollie Brooks
Parameters
xis the quantile and must be greater than 0.
ais the shape parameter and must be positive.
bis the rate parameter and must be positive.
Returns
a dvariable object $ \Sigma_i (-a_i \ln(b)+\ln(\Gamma(a_i))-(a_i-1)\ln(x_i)+b x_i) $
See Also

Definition at line 197 of file dgamma.cpp.

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