2017•Unpublished venueRequires access
Binomial Distribution
Myke King
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Abstract
The most well known discrete distribution is the binomial distribution. Equally well known, the Poisson distribution derives from the binomial distribution. This chapter describes the range of extensions to both. The binomial distribution gives the probability of a number of successes; the negative binomial distribution gives the probability of a number of failures. Also known as the Pascal distribution, it is also a special case of the Polya distribution. It is a compound distribution, starting as the Poisson distribution. But, instead of the expected number of successes (λ) being a constant, it is assumed to follow the gamma distribution. Like the negative binomial distribution, beta-negative binomial distribution gives the probability of a number of failures (x) before there are n successes, but with this assumed to follow the beta distribution. The beta-geometric distribution is a special case of the betanegative binomial distribution. It requires only one success after x failures.