Built-in Mathematica Symbol

NegativeBinomialDistribution

NegativeBinomialDistribution[n, p]
represents a negative binomial distribution with parameters n and p.

The probability for value x in a negative binomial distribution is for non-negative integers, and is zero otherwise. »

If n is a positive integer, NegativeBinomialDistribution[n, p] gives the distribution of the number of failures in a sequence of trials with success probability p before n successes occur.

Mean and variance of a negative binomial distribution:

Probability density function:

Mean and variance of a negative binomial distribution:

Probability density function:

Generate a set of pseudorandom numbers that have the negative binomial distribution:

Properties based on higher-order moments:

Second moment of a negative binomial distribution:

The

quantile of a negative binomial distribution with

and

:

The probability of at least 5 failures before 10 successes for

:

Plot the cumulative distribution function of a negative binomial distribution:

The probability of getting any real number except a non-negative integer is zero:

Moments can be obtained from the characteristic function:

Negative binomial is a mixture of PoissonDistribution and GammaDistribution:

NegativeBinomialDistribution is not defined when n is non-positive:

NegativeBinomialDistribution is not defined when p is not between zero and one:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: