Statistics Toolbox

Negative Binomial Distribution

The following sections provide an overview of the negative binomial distribution.

Background of the Negative Binomial Distribution.   The geometric distribution is a special case of the negative binomial distribution (also called the Pascal distribution). The geometric distribution models the number of successes before one failure in an independent succession of tests where each test results in success or failure.

In the negative binomial distribution the number of failures is a parameter of the distribution. The parameters are the probability of success, p, and the number of failures, r.

Definition of the Negative Binomial Distribution.   The negative binomial pdf is

where .

Example and Plot of the Negative Binomial Distribution.   The following commands generate a plot of the negative binomial pdf.

x = (0:10);
y = nbinpdf(x,3,0.5);
plot(x,y,'+')
set(gca,'XLim',[-0.5,10.5])

Lognormal Distribution

Normal Distribution