Probabilities.NegBinomPDF Function

Negative binomial probability density function (PDF).

Pascal

function NegBinomPDF(x: Integer; R: double; p: double): double; overload;

Parameters	Description
x	Function domain, integer, number of trials needed to obtain R successes.
R	Defines number of successes, positive integer.
p	Defines probability of each trial, real value on closed interval [0,1].

Returns

the negative binomial probability density function (PDF) for value x using the parameters R (number of success) and p (probability of success). Probability p must lie on the interval [0,1] and R must be greater or equal than one, otherwise the result is NAN.

Description

The negative binomial probability density function is defined by the following equation:

where I is the discrete interval on which the negative binomial PDF is not zero. The negative binomial distribution can be thought of as a "reversal" of the binomial distribution. In the binomial setting the random variable represents the number of successes obtained in a series on n independent and identical Bernoulli trials: the number of trials is fixed and the number of successes will vary from experiment to experiment. The negative binomial random variable represents the number of trials needed to obtain exactly R successes; here, the number of successes is fixed and the number of trials will vary from experiment to experiment. In particular, the negative binomial random variable arises in situations characterized by these properties:

The experiment consists of a series of independent and identical Bernoulli trials, each with probability p of success.
The trials are observed until exactly R successes are obtained, where R is fixed by the experimentator.
The random variable x is the number of trials needed to obtain the R successes.