The Distribution of a Sum of Independent Binomial Random Variables

Ken Butler and Michael A. Stephens ()
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Ken Butler: University of Toronto Scarborough
Michael A. Stephens: Simon Fraser University

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 2, 557-571

Abstract: Abstract The distribution of a sum S of independent binomial random variables, each with different success probabilities, is discussed. An efficient algorithm is given to calculate the exact distribution by convolution. Two approximations are examined, one based on a method of Kolmogorov, and another based on fitting a distribution from the Pearson family. The Kolmogorov approximation is given as an algorithm, with a worked example. The Kolmogorov and Pearson approximations are compared for several given sets of binomials with different sample sizes and probabilities. Other methods of approximation are discussed and some compared numerically. The Kolmogorov approximation is found to be extremely accurate, and the Pearson curve approximation useful if extreme accuracy is not required.

Keywords: Kolmogorov-type approximation; Pearson distributions; Gram-Charlier; Saddle-point; Reliability; Survival analysis; 62E17; 60K10; 90B25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11009-016-9533-4

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