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2012•Probability in the Engineering and Informational SciencesRequires access

A MIXTURE OF EXPONENTIAL AND IFR GAMMA DISTRIBUTIONS HAVING AN UPSIDEDOWN BATHTUB-SHAPED FAILURE RATE

Henry W. Block, Naftali A. Langberg, Thomas H. Savits

Open publisher page 8 citations

Abstract

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

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What this paper is about

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

Key concepts: Bathtub, Gamma distribution, Failure rate, Exponential function, Exponential distribution, Mathematics, Distribution (mathematics), Exponential family

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