MC::Distributions Namespace Reference

Kokkos compatible method to draw from specific probability distribution. More...

Classes
struct	Exponential
	Represents a Exponential probability distribution. More...
struct	LogNormal
	Represents a LogNormal (Gaussian) probability distribution. More...
struct	Normal
	Represents a normal (Gaussian) probability distribution. More...
struct	ScaledTruncatedNormal
	Represents a Scaled TruncatedNormal (Gaussian) probability distribution. More...
struct	SkewNormal
	Represents a SkewNormal (Gaussian) probability distribution. More...
struct	TruncatedNormal
	Represents a TruncatedNormal (Gaussian) probability distribution. More...
struct	Uniform

Concepts
concept	ProbabilityLaw
	Concept for probability distribution laws.

Functions
template<FloatingPointType F>
KOKKOS_INLINE_FUNCTION F	erfinv (F x)
	Computes an approximation of the inverse error function.
template<FloatingPointType F>
KOKKOS_INLINE_FUNCTION F	norminv (F p, F mean, F stddev)
	Computes the inverse CDF (probit function) of a normal distribution.
template<FloatingPointType F>
KOKKOS_INLINE_FUNCTION F	std_normal_pdf (F x)
	Computes the standard normal probability density function (PDF).
template<FloatingPointType F>
KOKKOS_INLINE_FUNCTION F	std_normal_cdf (F x)
	Computes the standard normal cumulative distribution function (CDF).

Detailed Description

Kokkos compatible method to draw from specific probability distribution.

Function Documentation

erfinv()

template<FloatingPointType F>

KOKKOS_INLINE_FUNCTION F MC::Distributions::erfinv

(

F

x

)

Computes an approximation of the inverse error function.

This function approximates the inverse error function erfinv(x) using Winitzki’s method (from A. Soranzo, E. Epure), which provides a simple and computationally efficient formula based on logarithms and square roots.

Template Parameters

F	Floating-point type (must satisfy FloatingPointType).

Parameters

x	Input value in the range [-1, 1].

Returns

Approximate value of erfinv(x).`.

Note

This implementation is not highly optimized for GPUs. For a more accurate and efficient implementation, see: https://people.maths.ox.ac.uk/gilesm/codes/erfinv/gems.pdf. See also bramowitz and Stegun method (Handbook of Mathematical Functions, formula 7.1.26)

Warning

This approximation is not valid for extreme values |x| close to 1.

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norminv()

template<FloatingPointType F>

KOKKOS_INLINE_FUNCTION F MC::Distributions::norminv	(	F	p,
		F	mean,
		F	stddev )

Computes the inverse CDF (probit function) of a normal distribution.

This function returns the quantile function of a normal distribution with mean mean and standard deviation stddev, given a probability p.

Template Parameters

F	Floating-point type (must satisfy FloatingPointType).

Parameters

p	Probability value in the range (0,1).
mean	Mean of the normal distribution.
stddev	Standard deviation of the normal distribution.

Returns

The corresponding value x such that P(X ≤ x) = p for X ~ N(mean, stddev).

Note

This implementation uses the inverse error function erfinv(x) for accuracy and efficiency. Extreme values may be clamped for stability.

Warning

p must be strictly in (0,1), otherwise the result is undefined.

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std_normal_cdf()

template<FloatingPointType F>

KOKKOS_INLINE_FUNCTION F MC::Distributions::std_normal_cdf

(

F

x

)

Computes the standard normal cumulative distribution function (CDF).

The standard normal CDF is given by:

\[ \Phi(x) = \frac{1}{2} \left( 1 + \operatorname{erf} \left( \frac{x}{\sqrt{2}} \right) \right) \]

Template Parameters

F	Floating-point type (must satisfy FloatingPointType).

Parameters

x	Input value.

Returns

Value of the standard normal CDF at x, which is P(X ≤ x) for X ~ N(0,1).

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std_normal_pdf()

template<FloatingPointType F>

KOKKOS_INLINE_FUNCTION F MC::Distributions::std_normal_pdf

(

F

x

)

Computes the standard normal probability density function (PDF).

The standard normal PDF is given by:

\[ \phi(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2 / 2} \]

Template Parameters

F	Floating-point type (must satisfy FloatingPointType).

Parameters

x	Input value.

Returns

Value of the standard normal PDF at x.

Note

This function is numerically stable.

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