Built-in Mathematica Symbol

BetaBinomialDistribution

BetaBinomialDistribution[

,

, n]
represents a beta binomial mixture distribution with beta distribution parameters

and

, and

binomial trials.

MORE INFORMATION

The beta binomial distribution is a binomial distribution with trials whose probability parameter p follows a beta distribution with shape parameters and . »

BetaBinomialDistribution allows and to be any positive real numbers, and n to be any positive integer.

BetaBinomialDistribution can be used with such functions as Mean, CDF and RandomInteger. »

EXAMPLES

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Basic Examples (2)

Mean and variance of a beta binomial distribution:

Probability density function:

Mean and variance of a beta binomial distribution:

Probability density function:

Scope (3)

Generate a set of pseudorandom numbers that have a beta binomial distribution:

Properties based on higher-order moments:

The

quantile of a beta binomial distribution with

,

and

:

Applications (3)

The probability of more than 50 successes in 100 trials assuming a beta distribution on p:

Plot the cumulative distribution function of a beta binomial distribution:

Density functions for beta binomial distributions depend heavily on the parameters

and

:

Properties & Relations (2)

The probability of getting negative integers, integers beyond n, or non-integer numbers is zero:

Beta binomial is a mixture of BinomialDistribution and BetaDistribution:

Possible Issues (3)

BetaBinomialDistribution is not defined when

or

is non-positive:

BetaBinomialDistribution is not defined when n is not a positive integer:

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