Sufficient Conditions for Some Stochastic Orders of Discrete Random Variables with Applications in Reliability

Abstract

In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the unimodality of the likelihood ratio for the comparison in some stochastic orders of two discrete random variables. These results have interest in comparing discrete random variables because the sufficient conditions are easy to check when there are no closed expressions for the survival functions, which occurs in many cases. In addition, the results are applied to compare several parametric families of discrete distributions.

On the Residual Lifetime and Inactivity Time in Mixtures

“…A number of papers [11][12][13][14][15][16][17][18][19][20][21][22] contain relevant results on this issue. Recent research concerning stochastic orders of discrete random variables can be found in [23].…”

“…Our description of the residual life variance and inactivity time variance follows the approach in [25] for the failure rate and that in [26] for the reversed hazard rate in mixtures. Both studies present a Bayesian perspective, based on the conditional distribution of the frailty given the data, which is different from that in [2][3][4][6][7][8][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Hence, the frailty cannot be observed but it can be updated.…”