On the negative binomial distribution and its generalizations
Copyright policy )On the negative binomial distribution and its generalizations
Some representations of the negative binomial distribution \(NB(r,p)\) are given. Specifically, it was proved that \(NB(r,p)\) may be represented, under suitable assumptions, as the distribution of: (a) the sum of dependendent geometric random variables; (b) the number of trials for the r-th success, based on a sequence of dependent Bernoulli random variables. Moreover, \(NB(2,p)\) may arise as the distribution of the sum of \(\mathbb Z^{+}\)-valued random variables that are neither geometric nor independent. Certain generalized negative binomial distributions are also investigated.
Sums Of Random Variables, Binomial Moments, Negative Binomial Distribution, Characterizations, sums of random variables, negative binomial distribution, Bernoulli sequences, 519, geometric distribution, binomial moments, Probabilistic Models, generalized negative binomial distributions, Bernoulli Sequences, Trials, Successes, probabilistic models, Number, characterizations, Characterization and structure theory of statistical distributions, Probability distributions: general theory, Geometric Distribution, Generalized Negative Binomial Distributions
Sums Of Random Variables, Binomial Moments, Negative Binomial Distribution, Characterizations, sums of random variables, negative binomial distribution, Bernoulli sequences, 519, geometric distribution, binomial moments, Probabilistic Models, generalized negative binomial distributions, Bernoulli Sequences, Trials, Successes, probabilistic models, Number, characterizations, Characterization and structure theory of statistical distributions, Probability distributions: general theory, Geometric Distribution, Generalized Negative Binomial Distributions
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