GeometricPDF Routines

Summary

Geometric probability density function (PDF).

Declaration

Procedure GeometricPDF(X: TDenseMtxVec; p: TSample; Res: TDenseMtxVec);

Description

Calculates the Geometric PDF for vector X using the parameter p. The results are stored in vector Res. The Res Length and Complex properties are adjusted automatically. If vector X is complex, an exception is raised.

Declaration

Function GeometricPDF(x: Integer; p: TSample): TSample;

Parameter	Description
x	Defines distribution parameter, valid on [0,INF) interval.
p	Defines distribution success probability parameter. p must lie on the [0,1] inverval.

Result

the geometric probability density function (PDF) for value x by using parameter p (probability).

Description

Calculates the geometric distribution probability density function, defined by the following equation:

where I is the discrete interval on which the geometric PDF is not zero. To recognize a situation that involves a geometrical random variable, following assumptions must be met:
- The experiment consist of series of trials. The outcome of each trial can be classed either as success or a failure. A trial with this property is called a Bernoulli trial.
- The trials are identical and independent in the sense that the outcome of one trial has no effect on the outcome of any other. The probability of success, p, remains the same from trial to trial.
- The random variable x denotes the number of trials needed to obtain the first success.
Parameters:

p: [0,1]

Support: x: [1,2,3,...)