The Distribution of a Sum of Independent Binomial Random Variables
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 o...
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| Veröffentlicht in: | Methodology and computing in applied probability 2017-06, Vol.19 (2), p.557-571 |
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| container_title | Methodology and computing in applied probability |
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| creator | Butler, Ken Stephens, Michael A. |
| description | 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. |
| doi_str_mv | 10.1007/s11009-016-9533-4 |
| format | Article |
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| ispartof | Methodology and computing in applied probability, 2017-06, Vol.19 (2), p.557-571 |
| issn | 1387-5841 1573-7713 |
| language | eng |
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| source | EBSCOhost Business Source Complete; SpringerLink Journals - AutoHoldings |
| subjects | Algorithms Approximation Binomial distribution Binomials Business and Management Convolution Economics Electrical Engineering Independent variables Life Sciences Mathematics and Statistics Probabilistic methods Random variables Statistics |
| title | The Distribution of a Sum of Independent Binomial Random Variables |
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