dc.contributor.author Hong,Yili en_US dc.date.accessioned 2019-05-08T19:46:18Z dc.date.available 2019-05-08T19:46:18Z dc.date.issued 2011-04-05 en dc.identifier.uri http://hdl.handle.net/10919/89411 dc.description.abstract The Poisson binomial distribution is the distribution of the sum of independent and non-identical random indicators. Each indicator follows a Bernoulli distribution with individual success probability. When all success probabilities are equal, the Poisson binomial distribution is a binomial distribution. The Poisson binomial distribution has many applications in different areas such as reliability, survival analysis, survey sampling, econometrics, etc. The computing of the cumulative distribution function (cdf) of the Poisson binomial distribution, however, is not straightforward. Approximation methods such as the Poisson approximation and normal approximations have been used in literature. Recursive formulae also have been used to compute the cdf in some areas. In this paper, we present a simple derivation for an exact formula with a closed-form expression for the cdf of the Poisson binomial distribution. The derivation uses the discrete Fourier transform of the characteristic function of the distribution. We develop an algorithm for efficient implementation of the exact formula. Numerical studies were conducted to study the accuracy of the developed algorithm and the accuracy of approximation methods. We also studied the computational efficiency of different methods. The paper is concluded with a discussion on the use of different methods in practice and some suggestions for practitioners. en dc.format.extent 17 pages en dc.format.mimetype application/pdf en dc.language.iso en en dc.publisher Virginia Tech en dc.relation.ispartofseries Technical Report No. 11-2 en dc.rights In Copyright (InC) en dc.rights This Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s). For other uses you need to obtain permission from the rights holder(s). en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject Characteristic function en dc.subject Discrete Fourier transform en dc.subject k-out-of-n system en dc.subject Normal approximation en dc.subject Poisson binomial distribution en dc.subject Warranty returns en dc.title On Computing the Distribution Function for the Sum of Independent and Non-identical Random Indicators en dc.type Technical report en dc.contributor.department Statistics en_US dc.type.dcmitype Text en dc.identifier.sourceurl https://www.stat.vt.edu/content/dam/stat_vt_edu/graphics-and-pdfs/research-papers/Technical_Reports/TechReport11-2.pdf en
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