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1996•Communication in Statistics- Theory and MethodsRequires access

On the number of successes in dependent trials

P. Vellaisamy

Open publisher page 21 citations

Abstract

A new approach to the study of the distributions of sums of n Bernoulli variables by conditional distributions is considered, This leads to a characterization of binomial distribution, and provides a simple approach to the study of generalized binomial distributions. We show that the binomial distribution and Poisson's binomial distribution can be derived as the distribution of sum of dependent Bernoulli random variables. Finally the problem of Poisson approximation to the generalized binomial distribution is investigated.

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What this paper is about

A new approach to the study of the distributions of sums of n Bernoulli variables by conditional distributions is considered, This leads to a characterization of binomial distribution, and provides a simple approach to the study of generalized binomial distributions. We show that the binomial distribution and Poisson's binomial distribution can be derived as the distribution of sum of dependent Bernoulli random variables. Finally the problem of Poisson approximation to the generalized binomial distribution is investigated.

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OpenAlex reports 21 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A new approach to the study of the distributions of sums of n Bernoulli variables by conditional distributions is considered, This leads to a characterization of binomial distribution, and provides a simple approach to the study of generalized binomial distributions. We show that the binomial distribution and Poisson's binomial distribution can be derived as the distribution of sum of dependent Bernoulli random variables. Finally the problem of Poisson approximation to the generalized binomial distribution is investigated.

Key concepts: Poisson binomial distribution, Negative binomial distribution, Binomial distribution, Continuity correction, Beta-binomial distribution, Beta negative binomial distribution, Compound Poisson distribution, Mathematics

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