LibRan  0.1
Pseudo-random number distribution generator
Functions
LRgaus.c File Reference

The Gaussian (Normal) distributions centered on m and width given by 2s. More...

#include <math.h>
#include "libran.h"
Include dependency graph for LRgaus.c:

Go to the source code of this file.

Functions

double LRd_gausbm_RAN (LR_obj *o)
 LRd_gausbm_RAN(LR_obj *o) - double random Gaussian/Normal distribution using the Box-Muller method. More...
 
double LRd_gausmar_RAN (LR_obj *o)
 LRd_gausmar_RAN(LR_obj *o) - double random Gaussian/Normal distribution using the Marsaglia method with acceptance-rejection. More...
 
double LRd_gaus_PDF (LR_obj *o, double x)
 LRd_gaus_PDF(LR_obj *o, double x) - double Gaussian/Normal probablity distribution function. More...
 
double LRd_gaus_CDF (LR_obj *o, double x)
 LRd_gaus_CDF(LR_obj *o, double x) - double Gaussian/Normal cumulative distribution function. More...
 
float LRf_gausbm_RAN (LR_obj *o)
 LRf_gausbm_RAN(LR_obj *o) - float random Gaussian/Normal distribution using the Box-Muller method. More...
 
float LRf_gausmar_RAN (LR_obj *o)
 LRf_gausmar_RAN(LR_obj *o) - float random Gaussian/Normal distribution using the Marsaglia method with acceptance-rejection. More...
 
float LRf_gaus_PDF (LR_obj *o, float x)
 LRf_gaus_PDF(LR_obj *o, float x) - float Gaussian/Normal probablity distribution function. More...
 
float LRf_gaus_CDF (LR_obj *o, float x)
 LRf_gaus_CDF(LR_obj *o, float x) - float Gaussian/Normal cumulative distribution function. More...
 

Detailed Description

The Gaussian (Normal) distributions centered on m and width given by 2s.

The pseudo-random numbers are distributed from a Gaussian or Normal (also Laplace-Gauss) distribution. The mean is given by m and variance = $ s^2 $. The normal distribution is a very common continuous probability distribution and is commonly called the bell curve.

\begin{eqnarray*} \mbox{PDF}(x) &= \frac{1}{\sqrt{2\pi s^2}} e^{-\frac{(x - m)^2}{2 s^2}} \\ \mbox{CDF}(x) &= \frac{1}{2} \left[ 1 + \mbox{erf}\left(\frac{x - m}{s\sqrt{2}}\right) \right] \end{eqnarray*}

The default is m = 0, s = 1; which is called the standard normal distribution.

GaussianNormalDistribution.png
The central limit theorem states that the sum of a large number of identically distributed independent random variates will have an approximately normal distribution.

Gaussian distributed random variates can be generated in a couple of methods. The first is the Box-Muller method which generates a pair of Gaussian distributed random variates by considering the 2-dimensional form of the Gaussian distribution. The polar form can yield itself to using the inverse CDF for generating the random variates. However, this requires using time-intensive math functions such as the sin, cos, log, and sqrt functions.

The second method uses the Marsagalia's polar method with acceptance/rejection for generating random variates confined to the unit circle centered on the origin with radius 1. This gives an acceptance ratio to be $\frac{\pi}{4} \approx 78.5\% $, but the method only uses a single sqrt, log, and division per generated pair. This simplicity may result in a faster generator despite the time to calculate rejected samples.

Definition in file LRgaus.c.

Function Documentation

◆ LRd_gaus_CDF()

double LRd_gaus_CDF ( LR_obj *  o,
double  x 
)

LRd_gaus_CDF(LR_obj *o, double x) - double Gaussian/Normal cumulative distribution function.

Parameters
oLR_obj object
xvalue
Returns
double CDF at x

Definition at line 146 of file LRgaus.c.

◆ LRd_gaus_PDF()

double LRd_gaus_PDF ( LR_obj *  o,
double  x 
)

LRd_gaus_PDF(LR_obj *o, double x) - double Gaussian/Normal probablity distribution function.

Parameters
oLR_obj object
xvalue
Returns
double PDF at x

Definition at line 129 of file LRgaus.c.

◆ LRd_gausbm_RAN()

double LRd_gausbm_RAN ( LR_obj *  o)

LRd_gausbm_RAN(LR_obj *o) - double random Gaussian/Normal distribution using the Box-Muller method.

Default values: mean m = 0, std.deviation s = 1

Parameters
oLR_obj object
Returns
double

Definition at line 72 of file LRgaus.c.

◆ LRd_gausmar_RAN()

double LRd_gausmar_RAN ( LR_obj *  o)

LRd_gausmar_RAN(LR_obj *o) - double random Gaussian/Normal distribution using the Marsaglia method with acceptance-rejection.

Default values: mean m = 0, std.deviation s = 1

Parameters
oLR_obj object
Returns
double

Definition at line 101 of file LRgaus.c.

◆ LRf_gaus_CDF()

float LRf_gaus_CDF ( LR_obj *  o,
float  x 
)

LRf_gaus_CDF(LR_obj *o, float x) - float Gaussian/Normal cumulative distribution function.

Parameters
oLR_obj object
xvalue
Returns
float CDF at x

Definition at line 238 of file LRgaus.c.

◆ LRf_gaus_PDF()

float LRf_gaus_PDF ( LR_obj *  o,
float  x 
)

LRf_gaus_PDF(LR_obj *o, float x) - float Gaussian/Normal probablity distribution function.

Parameters
oLR_obj object
xvalue
Returns
float PDF at x

Definition at line 221 of file LRgaus.c.

◆ LRf_gausbm_RAN()

float LRf_gausbm_RAN ( LR_obj *  o)

LRf_gausbm_RAN(LR_obj *o) - float random Gaussian/Normal distribution using the Box-Muller method.

Default values: mean m = 0, std.deviation s = 1

Parameters
oLR_obj object
Returns
float

Definition at line 165 of file LRgaus.c.

◆ LRf_gausmar_RAN()

float LRf_gausmar_RAN ( LR_obj *  o)

LRf_gausmar_RAN(LR_obj *o) - float random Gaussian/Normal distribution using the Marsaglia method with acceptance-rejection.

Default values: mean m = 0, std.deviation s = 1

Parameters
oLR_obj object
Returns
float

Definition at line 193 of file LRgaus.c.

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