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# BetaNegativeBinomialDistribution

 BetaNegativeBinomialDistribution represents a beta negative binomial mixture distribution with beta distribution parameters and , and n successful trials.
• The beta negative binomial distribution is a negative binomial distribution whose probability parameter p follows a beta distribution with shape parameters and . »
Probability density function:
Cumulative distribution function:
Mean and variance:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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 Scope   (7)
Generate a set of pseudorandom numbers that have a beta negative binomial distribution:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Skewness:
Kurtosis:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
CDF of BetaNegativeBinomialDistribution is an example of a right continuous function:
The probability of at least 50 failures before 10 successes, assuming a beta distribution on :
The probability of getting negative integers, integers beyond n, or non-integer numbers is zero:
Relationships to other distributions:
WaringYuleDistribution is a special case of beta negative binomial distribution:
WaringYuleDistribution is a special case of beta negative binomial distribution:
Beta negative binomial distribution is a mixture of NegativeBinomialDistribution and BetaDistribution:
BetaNegativeBinomialDistribution is not defined when , , or n is non-positive:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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