RiskNegbin

Description

RiskNegbin(s,p) specifies a negative binomial distribution parameters s and p. This distribution is typically used to model the number of failures before achieving s successes in independent, identical trials, each with probability p of success. (The geometric distribution is a special case with s=1.) It is sometimes used in models of quality control and production testing, breakdown, and maintenance modelling.

Examples

RiskNegbin(5,.25) returns a negative binomial distribution with 5 successes and a 25% probability of success on each trial.

RiskNegbin(A6,A7) returns a negative binomial distribution with the number of successes taken from cell A6 and the probability of success taken from cell A7.

Guidelines

s must be a positive integer less than or equal to 32,767.

p must be between 0 and 1 (0 is disallowed, 1 is allowed).

Parameters

S        The number of successes
          discrete parameter                          

p        Probability of a single success
          continuous parameter                     

Domain

     discrete integers

Mass and Cumulative Distribution Functions

Here, ( ) is the Binomial Coefficient.

Mean

Variance

Skewness

for ,

Kurtosis

for ,

Mode

(bimodal)      z and z + 1      integer z > 0

(unimodal)      0                    integer z < 0

(unimodal)      smallest integer grearter than z       otherwise

Examples