Negative Binomial Distribution Calculator
Calculate the probability of achieving r successes by trial n.
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Enter the desired number of successes (r), the trial number (n), and the probability of success on each trial (p). The calculator computes the probability that the rth success occurs exactly on trial n.
About This Calculator
The negative binomial distribution models the number of trials needed to achieve a specified number of successes. It generalizes the geometric distribution (which is the special case r=1). Applications include modeling the number of sales calls needed to close r deals, or the number of experiments until r successful results.
Frequently Asked Questions
How is this different from the binomial distribution?
The binomial fixes the number of trials and asks how many successes. The negative binomial fixes the number of successes and asks how many trials are needed.
What is the mean of the negative binomial?
The mean number of trials is r/p. If you need 3 successes with p=0.3, expect about 10 trials on average.
Why is it called negative binomial?
The name comes from the mathematical connection to the binomial theorem with negative exponents used in deriving the distribution.