Sample a power distribution for powers not equal to -1. More...

#include <PowerDistribution.hh>

Public Member Functions
CELER_FUNCTION	PowerDistribution (real_type p)
	Construct on the interval [0, 1).

CELER_FUNCTION	PowerDistribution (real_type p, real_type a, real_type b)
	Construct on the interval [a, b).

template<class Generator >
CELER_FUNCTION result_type	operator() (Generator &rng) const

template<class Generator >
CELER_FUNCTION auto	operator() (Generator &rng) const -> result_type
	Sample a random number according to the distribution.

Detailed Description

template<class RealType = ::celeritas::real_type>
class celeritas::PowerDistribution< RealType >

Sample a power distribution for powers not equal to -1.

This distribution for a power \( p != -1 \) is defined on a positive range \( [a, b) \) and has the normalized PDF:

\[ f(x; p, a, b) = x^{p}\frac{p + 1}{b^{p + 1} - a^{p + 1}} \quad \mathrm{for } a < x < b \]

which integrated into a CDF and inverted gives a sample:

\[ x = \left[ (b^{p + 1} - a^{p + 1})\xi + a^{p + 1} \right]^{1/(p + 1)} \]

The quantity in brackets is a uniform sample on \( [a^{p + 1}, b^{p + 1}) \)

See C13A (and C15A) from everett-montecarlo-1972 , with \( x \gets u \), \( p \gets m - 1 \).

Note: For \( p = -1 \) see ReciprocalDistribution , and in the degenerate case of \( p = 0 \) this is mathematically equivalent to UniformRealDistribution .

Constructor & Destructor Documentation

template<class RealType >

CELER_FUNCTION celeritas::PowerDistribution< RealType >::PowerDistribution	(	real_type	p,
		real_type	a,
		real_type	b
	)

inline

Construct on the interval [a, b).

It is allowable for the two bounds to be out of order.

The documentation for this class was generated from the following file: