## 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 etal. (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.

Original language | English |
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Pages (from-to) | 176-180 |

Number of pages | 5 |

Journal | Statistics and Probability Letters |

Volume | 94 |

DOIs | |

State | Published - 1 Nov 2014 |

### Bibliographical note

Publisher Copyright:© 2014 .

## Keywords

- Convolution
- Decreasing failure rate
- Failure rate function
- Gamma densities
- Increasing failure rate
- Reliability

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty