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dc.contributor.authorHong,Yilien_US
dc.date.accessioned2019-05-08T19:46:18Z
dc.date.available2019-05-08T19:46:18Z
dc.date.issued2011-04-05en
dc.identifier.urihttp://hdl.handle.net/10919/89411
dc.description.abstractThe 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.extent17 pagesen
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.ispartofseriesTechnical Report No. 11-2en
dc.rightsIn Copyright (InC)en
dc.rightsThis 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.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCharacteristic functionen
dc.subjectDiscrete Fourier transformen
dc.subjectk-out-of-n systemen
dc.subjectNormal approximationen
dc.subjectPoisson binomial distributionen
dc.subjectWarranty returnsen
dc.titleOn Computing the Distribution Function for the Sum of Independent and Non-identical Random Indicatorsen
dc.typeTechnical reporten
dc.contributor.departmentStatisticsen_US
dc.type.dcmitypeTexten
dc.identifier.sourceurlhttps://www.stat.vt.edu/content/dam/stat_vt_edu/graphics-and-pdfs/research-papers/Technical_Reports/TechReport11-2.pdfen


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