The Binomial distribution with probability of success p > 0 and n independent tests. More...

#include <math.h>
#include "libran.h"

Include dependency graph for LRbinom.c:

Functions
int	LRi_binomial_RAN (LR_obj *o)
	LRi_binomial_RAN(LR_obj *o) - int Binomial distributed variate. Default values: probability of success p = 1/2. More...

float	LRi_binomial_PDF (LR_obj *o, int k)
	LRi_binomial_PDF(LR_obj *o, int k) - Binomial probablity (or mass) distribution function. More...

float	LRi_binomial_CDF (LR_obj *o, int k)
	LRi_binomial_CDF(LR_obj *o, int k) - Binomial distribution cumulative distribution function. More...

Detailed Description

The Binomial distribution with probability of success p > 0 and n independent tests.

The pseudo-random numbers are distributed from the Binomial distribution, which is a discrete distribution describing the number of successful Bernoulli trails in n events. A Bernoulli trial is one characterized by either "success" or "failure." For example, n coin flips where the number of heads is shown is described by the Bimomial distribution. If n is large and p not "extreme" then the distribution will approach the Normal distribution, and these routines may not be as effective. This approach to a Normal distribution is established by the "central limit theorem."

The attribute p is greater than zero and less than one and represents the probability of a successful trial. Therefore, np is the mean number of successful trials in n events and also may not be an integer value.

$\begin{eqnarray*} \mbox{PDF}(k) &= \left. \begin{array}{ll} \left(\begin{array}{c} {n} \\ {k} \end{array}\right) p^k (1-p)^{n-k}, & 0 \le k \le n \end{array} \right. \\ \\ \mbox{CDF}(k) &= \left. \begin{array}{ll} \sum_{i=0}^{k} \left(\begin{array}{c} {n} \\ {i} \end{array}\right) p^i (1-p)^{n-i}, & 0 \le k \le n \end{array} \right. \end{eqnarray*}$

The default is $p = \frac{1}{2}$ and q will be set to $\frac{1}{\log(1-p)}$ for calculation efficiency. Do not set q when declaring this distribution.

The plots show the distribution functions as continuous only to visually connect adjacent values but are actually discrete.

See also: LRgaus.c LRgsn.c LRgeom.c

Definition in file LRbinom.c.

Function Documentation

◆ LRi_binomial_CDF()

float LRi_binomial_CDF	(	LR_obj *	o,
		int	k
	)

LRi_binomial_CDF(LR_obj *o, int k) - Binomial distribution cumulative distribution function.

Parameters

o	LR_obj object
x	value

Returns: float CDF at x

Definition at line 133 of file LRbinom.c.

◆ LRi_binomial_PDF()

float LRi_binomial_PDF	(	LR_obj *	o,
		int	k
	)

LRi_binomial_PDF(LR_obj *o, int k) - Binomial probablity (or mass) distribution function.

Parameters

o	LR_obj object
x	value

Returns: float PDF at x

Definition at line 108 of file LRbinom.c.

◆ LRi_binomial_RAN()

int LRi_binomial_RAN ( LR_obj * o )

LRi_binomial_RAN(LR_obj *o) - int Binomial distributed variate. Default values: probability of success p = 1/2.

The random variate is generated using the waiting time property - Generate a number of exponential variates until the waited sum exceeds some value.

Parameters

o	LR_obj object

Returns: int

Definition at line 82 of file LRbinom.c.

Functions

Detailed Description

Function Documentation

◆ LRi_binomial_CDF()

◆ LRi_binomial_PDF()

◆ LRi_binomial_RAN()