A stochastic inequality for the largest order statistics from heterogeneous gamma variables

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 denote the corresponding largest order statistic. Let Yn:n denote the largest order statistic arising from independent and identically distributed gamma random …