The Exponentially Modified Gaussian Distribution

Utilities for working with the Exponentially Modified Gaussian Distribution

Functions
template<typename realT>
realT	mx::math::func::expModGaussian (realT x, realT mu, realT sigma, realT lambda)
	The Exponentially Modified Gaussian at a point.
template<typename realT>
realT	mx::math::func::expModGaussianMean (realT mu, realT lambda)
	The Mean of the Exponentially Modified Gaussian.
template<typename realT>
realT	mx::math::func::expModGaussianVariance (realT sigma, realT lambda)
	The Variance of the Exponentially Modified Gaussian.
template<typename realT>
realT	mx::math::func::expModGaussianMode (realT mu, realT sigma, realT lambda)
	The Mode of the Exponentially Modified Gaussian.

Function Documentation

expModGaussian()

template<typename realT>

realT mx::math::func::expModGaussian	(	realT	x,
		realT	mu,
		realT	sigma,
		realT	lambda )

The Exponentially Modified Gaussian at a point.

Calculates the value of the Exponentially Modified Gaussian distribution at a location specified by x.

Template Parameters

realT

a real floating point type

Returns

the value of the Exponentially Modified Gaussian distribution at x.

Parameters

[in]	x	the location at which to calculate the distribution
[in]	mu	the mean parameter
[in]	sigma	the standard deviation
[in]	lambda	the rate of decay

Definition at line 54 of file expModGaussian.hpp.

References mx::math::root_two().

expModGaussianMean()

template<typename realT>

realT mx::math::func::expModGaussianMean	(	realT	mu,
		realT	lambda )

The Mean of the Exponentially Modified Gaussian.

Calculates the mean of the Exponentially Modified Gaussian distribution.

Template Parameters

realT

a real floating point type

Returns

the mean of the Exponentially Modified Gaussian.

Parameters

[in]	mu	the mean parameter
[in]	lambda	the rate of decay

Definition at line 75 of file expModGaussian.hpp.

Referenced by expModGaussianMode().

expModGaussianMode()

template<typename realT>

realT mx::math::func::expModGaussianMode	(	realT	mu,
		realT	sigma,
		realT	lambda )

The Mode of the Exponentially Modified Gaussian.

Calculates the mode of the Exponentially Modified Gaussian distribution. This is done iteratively with Brent's method.

Template Parameters

realT

a real floating point type

Returns

the mode of the Exponentially Modified Gaussian.

Parameters

[in]	mu	the mean parameter
[in]	sigma	the standard deviation
[in]	lambda	the rate of decay

Definition at line 124 of file expModGaussian.hpp.

References expModGaussianMean(), and expModGaussianVariance().

expModGaussianVariance()

template<typename realT>

realT mx::math::func::expModGaussianVariance	(	realT	sigma,
		realT	lambda )

The Variance of the Exponentially Modified Gaussian.

Calculates the variance of the Exponentially Modified Gaussian distribution.

Template Parameters

realT

a real floating point type

Returns

the variance of the Exponentially Modified Gaussian.

Parameters

[in]	sigma	the standard deviation
[in]	lambda	the rate of decay

Definition at line 93 of file expModGaussian.hpp.

Referenced by expModGaussianMode().