Expand Your Knowledge: Negative Binomial Distribution

Expand Your Knowledge: Negative Binomial Distribution Suppose you have binomial trials for which the probability of success on each trial is p and the probability of failure is q = 1 - p. Let k be a fixed whole number greater than or equalto 1. Let n be the number of the trial on which the kth success occurs. This means that the first  k – 1  successes occur within the first n – 1 trials, while the kth success actually occurs on the nth trial. Now, if we are going to have k successes, we must have at least k trials. So, n = k, k = 1, k = 2,  . . . and n is a random variable. In the literature of mathematical statistics, the probability distribution for n is called thenegative binomial distribution.