Mean residual life order of convolutions of heterogeneous exponential random variables

Authors:
Peng Zhao;N. Balakrishnan
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 3
Cited 7

Schur properties of convolutions of exponential and geometric random variables

Journal of Multivariate Analysis
On stochastic orders for sums of independent random variables

Journal of Multivariate Analysis
Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables

Journal of Multivariate Analysis

On the right spread order of convolutions of heterogeneous exponential random variables

Journal of Multivariate Analysis
On hazard rate ordering of the sums of heterogeneous geometric random variables

Journal of Multivariate Analysis
Ordering convolutions of heterogeneous exponential and geometric distributions revisited

Probability in the Engineering and Informational Sciences
Some new results on convolutions of heterogeneous gamma random variables

Journal of Multivariate Analysis
On skewness and dispersion among convolutions of independent gamma random variables

Probability in the Engineering and Informational Sciences
Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

Journal of Multivariate Analysis
On sample ranges in multiple-outlier models

Journal of Multivariate Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study convolutions of heterogeneous exponential random variables with respect to the mean residual life order. By introducing a new partial order (reciprocal majorization order), we prove that this order between two parameter vectors implies the mean residual life order between convolutions of two heterogeneous exponential samples. For the 2-dimensional case, it is shown that there exists a stronger equivalence. We discuss, in particular, the case when one convolution involves identically distributed variables, and show in this case that the mean residual life order is actually associated with the harmonic mean of parameters. Finally, we derive the ''best gamma bounds'' for the mean residual life function of any convolution of exponential distributions under this framework.