negative binomial distribution

Let us learn about negative binomial distribution

--> The discrete probability distribution of number of successes in a sequence of Bernoulli trials is negative binomial distribution when number of failures occurs before the trials. It has special cases. They are Pascal distribution and Poly distribution. Pascal based on integer valued parameter and Polya based on real valued case. The negative binomial distribution is X ˜ NB(r,p). This equation based on Bernoulli trials that is each trial give the two outcomes. They are “success” and “failure”.
Negative binomial distribution:
The outcomes need not associated with word “success” and “failure” when we apply the real world situations. We only get the outcome as good or bad. The negative binomial distribution with probability mass function is

f(k) = Pr(X = k) = (K+r-1) (1-p)^r p^k for k=0,1,2......

r-1

Binomial coefficient is represented within paranthesis.



We can extend the negative binomial distribution to real valued r’s. Similarly we can’t visualize the number of failures in non integer number.