The limiting failure rate for a convolution of gamma distributions

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

Statistics & Probability Letters, 2014, vol. 94, issue C, 176-180

Abstract: In this paper we investigate the limiting behavior of the failure rate for the convolution of two or more gamma distributions. In a related paper, Block et al. (2014) show that the limiting failure rate of a convolution of life distributions behaves like the limiting failure rate of the strongest component. The proof of this general result, however, does not cover the case when the strongest component has an unbounded failure rate such as in the case of a DFR gamma distribution. A proof is given here for the convolution of m gamma densities which covers the DFR case. We first show that the convolution can be expressed as an infinite mixture of gamma densities.

Keywords: Reliability; Failure rate function; Increasing failure rate; Decreasing failure rate; Convolution; Gamma densities (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2014.06.018

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