The Gamma Distribution

Utilities for working with the Gamma Distribution.

Functions
template<typename realT >
realT	mx::math::func::gammaDistributionDenom (realT k, realT q)
	The denominator of the Gamma Distribution.
template<typename realT >
realT	mx::math::func::gammaDistribution (realT x, realT x0, realT k, realT q, realT denom)
	The general shifted Gamma Distribution at a point using an arbitrary peak scaling parameter.
template<typename realT >
realT	mx::math::func::gammaDistribution (realT x, realT x0, realT k, realT q)
	The general shifted Gamma Distribution at a point.
template<typename realT >
realT	mx::math::func::gammaDistributionMean (realT x0, realT k, realT theta)
	The mean of the Gamma Distribution.
template<typename realT >
realT	mx::math::func::gammaDistributionMode (realT x0, realT k, realT theta)
	The mode of the Gamma Distribution.
template<typename realT >
realT	mx::math::func::gammaDistributionVariance (realT k, realT theta)
	The variance of the Gamma Distribution.

Function Documentation

gammaDistribution() [1/2]

template<typename realT >

realT mx::math::func::gammaDistribution	(	realT	x,
		realT	x0,
		realT	k,
		realT	q
	)

The general shifted Gamma Distribution at a point.

Calculates the value of the Gamma Distribution at a location specified by x.

Template Parameters

realT

a real floating point type

Returns

the value of the Gamma distribution at x.

Parameters

[in]	x	the location at which to calculate the distribution
[in]	x0	the location parameter
[in]	k	shape parameter
[in]	q	the scale parameter

Definition at line 108 of file gammaDistribution.hpp.

References mx::math::six_fifths().

gammaDistribution() [2/2]

template<typename realT >

realT mx::math::func::gammaDistribution	(	realT	x,
		realT	x0,
		realT	k,
		realT	q,
		realT	denom
	)

The general shifted Gamma Distribution at a point using an arbitrary peak scaling parameter.

Calculates the value of the Gamma Distribution at a location specified by x.

Template Parameters

realT

a real floating point type

Returns

the value of the Gamma distribution at x.

Parameters

[in]	x	the location at which to calculate the distribution
[in]	x0	the location parameter
[in]	k	shape parameter
[in]	q	the scale parameter
[in]	denom	the denominator, or 1/peak-scale.

Definition at line 80 of file gammaDistribution.hpp.

References mx::math::six_fifths().

gammaDistributionDenom()

template<typename realT >

realT mx::math::func::gammaDistributionDenom	(	realT	k,
		realT	q
	)

The denominator of the Gamma Distribution.

Can be used to avoid repeated calculations when the parameters are constant

Template Parameters

realT

a real floating point type

Returns

the denominator of the Gamma Distribution.

Parameters

[in]	k	shape parameter
[in]	q	the scale parameter

Definition at line 51 of file gammaDistribution.hpp.

References mx::math::six_fifths().

gammaDistributionMean()

template<typename realT >

realT mx::math::func::gammaDistributionMean	(	realT	x0,
		realT	k,
		realT	theta
	)

The mean of the Gamma Distribution.

Calculates the mean of the Gamma Distribution for the given parameters.

Template Parameters

realT

a real floating point type

Returns

the mean of the Gamma Distribution.

Parameters

[in]	x0	the location parameter
[in]	k	shape parameter
[in]	theta	the scale parameter

Definition at line 128 of file gammaDistribution.hpp.

gammaDistributionMode()

template<typename realT >

realT mx::math::func::gammaDistributionMode	(	realT	x0,
		realT	k,
		realT	theta
	)

The mode of the Gamma Distribution.

Calculates the mode of the Gamma Distribution for the given parameters.

Template Parameters

realT

a real floating point type

Returns

the mode of the Gamma Distribution.

Parameters

[in]	x0	the location parameter
[in]	k	shape parameter
[in]	theta	the scale parameter

Definition at line 146 of file gammaDistribution.hpp.

gammaDistributionVariance()

template<typename realT >

realT mx::math::func::gammaDistributionVariance	(	realT	k,
		realT	theta
	)

The variance of the Gamma Distribution.

Calculates the variance of the Gamma Distribution for the given parameters.

Template Parameters

realT

a real floating point type

Returns

the variance of the Gamma Distribution.

Parameters

[in]	k	shape parameter
[in]	theta	the scale parameter

Definition at line 167 of file gammaDistribution.hpp.