The Weibull Distribution

Utilities for working with the Weibull Distribution.

Functions
template<typename realT >
realT	mx::math::func::weibull_lambda (std::vector< realT > &x, realT k, realT x0=0)
	The MLE of the Weibull distribution lambda parameter. More...
template<typename realT >
realT	mx::math::func::weibull (realT x, realT x0, realT k, realT lambda)
	The general shifted Weibull distribution at a point. More...
template<typename realT >
realT	mx::math::func::weibull (realT x, realT k, realT lambda)
	The Weibull distribution at a point. More...

Function Documentation

weibull() [1/2]

template<typename realT >

realT mx::math::func::weibull	(	realT	x,
		realT	k,
		realT	lambda
	)

The Weibull distribution at a point.

Calculates the value of the Weibull distribution at a location specified by x.

\[ f(x; \lambda, k) = \begin{cases} \frac{k}{\lambda}\left( \frac{x}{\lambda}\right)^{k-1} \exp \left( -\left(\frac{x}{\lambda}\right)^k \right), & x \ge 0 \\ 0, & x < 0 \end{cases} \]

Template Parameters

realT

a real floating point type

Returns

the value of the Weibull distribution at x.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters

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

Definition at line 116 of file weibull.hpp.

References mx::astro::constants::k().

weibull() [2/2]

template<typename realT >

realT mx::math::func::weibull	(	realT	x,
		realT	x0,
		realT	k,
		realT	lambda
	)

The general shifted Weibull distribution at a point.

Calculates the value of the Weibull distribution at a location specified by x.

\[ f(x; x_o, \lambda, k) = \begin{cases} \frac{k}{\lambda}\left( \frac{x-x_o}{\lambda}\right)^{k-1} \exp \left( -\left(\frac{x-x_o}{\lambda}\right)^k \right), & x \ge 0 \\ 0, & x < 0 \end{cases} \]

Template Parameters

realT

a real floating point type

Returns

the value of the Weibull distribution at x.

Parameters

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

Definition at line 81 of file weibull.hpp.

References mx::astro::constants::k().

weibull_lambda()

template<typename realT >

realT mx::math::func::weibull_lambda	(	std::vector< realT > &	x,
		realT	k,
		realT	x0 = 0
	)

The MLE of the Weibull distribution lambda parameter.

Template Parameters

realT

a real floating point type

Returns

the MLE of lambda given the data.

Parameters

[in]	x	the data points
[in]	k	the shape parameter
[in]	x0	[optional] the location parameter

Definition at line 46 of file weibull.hpp.

References mx::astro::constants::k().