Negative Binomial

Negative binomial distribution is a statistical discrete probability distribution, also known as Pascal or Boliye distribution. It is used for the analysis of counting data and has an integer probability from 0 to infinity. Negative binomial distribution is similar to Bernoulli test, but different from Bernoulli test, it indicates the number of times of success, while negative binomial represents the number of times of failure that occurs at the beginning of the sequence until a given number of successes are achieved; it is different from Poisson distribution whose permissible conditions change beyond the conditional mean. Negative binomial distribution is a process.

Negative binomial distribution formula:

Negative binomial distribution P (X = r) = n-1Cr-1p R (1-p) N-R

Here the combination of n-1Cr-1 = ((n-1)!/ ((n-1) - (r-1)!) / (r-1)!