Mean residual life order of convolutions of heterogeneous exponential random variables

Peng Zhao and N. Balakrishnan

Journal of Multivariate Analysis, 2009, vol. 100, issue 8, 1792-1801

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.

Keywords: Stochastic; order; Hazard; rate; order; Likelihood; ratio; order; Majorization; Reciprocal; majorization; order (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (8)

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