Some results on discrete mixture failure rates

Abstract

Some properties of the discrete mixture failure rates are studied. Specifically, similar to the continuous case, it is shown that the population mixture failure rate is always smaller than the unconditional expectation in the family of subpopulations failure rates. The analog of the multiplicative and the additive frailty models is introduced via the corresponding survival function. Another approach via the alternative discrete failure rate is also discussed. Stochastic comparisons for two mixed distributions with equal and different mixing distributions are studied. © 2018, © 2018 Taylor & Francis Group, LLC.