prrng::normal_distribution Class Reference

Normal distribution. More...

#include <prrng.h>

Public Member Functions
	normal_distribution (double mu=0, double sigma=1)
	Constructor.
template<class T >
T	pdf (const T &x)
	Probability density function.
template<class T >
T	cdf (const T &x)
	Cumulative density function.
template<class T >
T	quantile (const T &p)
	Quantile (the inverse of the cumulative density function).

Detailed Description

Normal distribution.

References:

• https://en.wikipedia.org/wiki/Normal_distribution
• https://www.boost.org/doc/libs/1_63_0/libs/math/doc/html/math_toolkit/sf_erf/error_inv.html
• https://www.boost.org/doc/libs/1_78_0/boost/math/special_functions/detail/erf_inv.hpp

Definition at line 1593 of file prrng.h.

Constructor & Destructor Documentation

normal_distribution()

prrng::normal_distribution::normal_distribution ( double  mu = 0, double  sigma = 1  )

inline

Constructor.

Parameters

mu	Average.
sigma	Standard deviation.

Definition at line 1601 of file prrng.h.

Member Function Documentation

cdf()

template<class T >

T prrng::normal_distribution::cdf ( const T &  x )

inline

Cumulative density function.

\( \Phi(x) = \frac{1}{2} \left[ 1 + \mathrm{erf}\left( \frac{x - \mu}{\sigma \sqrt{2}} \right) \right] \)

Parameters

x	Coordinates.

Returns

Cumulative density for each x.

Definition at line 1634 of file prrng.h.

pdf()

template<class T >

T prrng::normal_distribution::pdf ( const T &  x )

inline

Probability density function.

Parameters

x	Coordinates.

Returns

Probability density for each x.

Definition at line 1615 of file prrng.h.

quantile()

template<class T >

T prrng::normal_distribution::quantile ( const T &  p )

inline

Quantile (the inverse of the cumulative density function).

For a given probability \( p \) the output is

\( x = \mu + \sigma \sqrt{2} \mathrm{erf}^{-1} (2p - 1) \)

Parameters

p	Probability [0, 1].

Returns

Quantile for each p.

Definition at line 1649 of file prrng.h.

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

• prrng.h