# 32. Negative Binomial Distribution

1. Catherine Forbes1,
2. Merran Evans1,
3. Nicholas Hastings2 and
4. Brian Peacock3

Published Online: 16 DEC 2010

DOI: 10.1002/9780470627242.ch32

## Statistical Distributions, Fourth Edition

#### How to Cite

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2010) Negative Binomial Distribution, in Statistical Distributions, Fourth Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470627242.ch32

#### Author Information

1. 1

Monash University, Victoria, Australia

2. 2

Albany Interactive, Victoria, Australia

3. 3

Brian Peacock Ergonomics, SIM University, Singapore

#### Publication History

1. Published Online: 16 DEC 2010
2. Published Print: 29 NOV 2010

#### ISBN Information

Print ISBN: 9780470390634

Online ISBN: 9780470627242

## SEARCH

### Keywords:

• negative binomial distribution;
• parameter estimation;
• Pascal variate;
• probability function;
• random number

### Summary

The Pascal variate is the number of failures before the xth success in a sequence of Bernoulli trials, where the probability of success at each trial is p and the probability of failure is q = 1 - p. This generalizes to the negative binomial variate for noninteger x. The Pascal distribution generalizes to the negative binomial, when the definition of “success” is not an integer. The Pascal variate is a special case of the negative binomial variate with integer values only. An alternative form of the Pascal variate involves trials up to and including the xth success. This chapter illustrates the probability function for the NB : x, p variate for selected values of x and p. It discusses variate relationships, parameter estimation and random number generation for the negative binomial distribution.

#### Controlled Vocabulary Terms

control variate; negative binomial distribution; probability