In this paper, we study the convolutions of heterogeneous exponential and geometric random variables in terms of the weakly majorization order () of parameter vectors and the likelihood ratio order (=lr). It is proved that order between two parameter vectors implies =lr order between...

Let X1,...,Xn be independent exponential random variables with respective hazard rates [lambda]1,...,[lambda]n, and let Y1,...,Yn be independent exponential random variables with common hazard rate [lambda]. This paper proves that X2:n, the second order statistic of X1,...,Xn, is larger than...

In this paper, we study ordering properties of convolutions of heterogeneous Erlang and Pascal random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [hazard rate order, mean residual life order]. We...

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...

In this paper, we study the inactive record values and carry out a stochastic comparison of these quantities from two independent samples. The results established here strengthen those of Amiripour et al. [Amiripour, F., Khaledi, B.-E., Hu, T., Shojaei, R., 2009. Some new results on...

This paper discusses ordering properties of lifetimes of parallel systems with two independent heterogeneous gamma components in terms of dispersive and star orders. It is proved, among others, that the p-larger order between the two scale vectors implies the dispersive order and the star order...

In this paper, we compare the largest order statistics arising from independent heterogeneous gamma random variables based on the likelihood ratio order. Let X1,…,Xn be independent gamma random variables with Xi having shape parameter r∈(0,1] and scale parameter λi, i=1,…,n, and let Xn:n...