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In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable X equal to the number of failures needed to get r successes in a sequence of independent Bernoulli trials where the probability p of success on each trial, while constant within any given experiment, is itself a random variable following a beta distribution, varying between different experiments. Thus the distribution is a compound probability distribution. If parameters of the beta distribution are α and β, and if where

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  • Beta negative binomial distribution (en)
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  • In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable X equal to the number of failures needed to get r successes in a sequence of independent Bernoulli trials where the probability p of success on each trial, while constant within any given experiment, is itself a random variable following a beta distribution, varying between different experiments. Thus the distribution is a compound probability distribution. If parameters of the beta distribution are α and β, and if where (en)
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  • In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable X equal to the number of failures needed to get r successes in a sequence of independent Bernoulli trials where the probability p of success on each trial, while constant within any given experiment, is itself a random variable following a beta distribution, varying between different experiments. Thus the distribution is a compound probability distribution. This distribution has also been called both the inverse Markov-Pólya distribution and the generalized Waring distribution. A shifted form of the distribution has been called the beta-Pascal distribution. If parameters of the beta distribution are α and β, and if where then the marginal distribution of X is a beta negative binomial distribution: In the above, NB(r, p) is the negative binomial distribution and B(α, β) is the beta distribution. (en)
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