Abstract
Let be independent non negative random variables with , i = 1, …, n, where λi > 0, i = 1, …, n and F is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic Xλn: n is smaller than another one Xθn: n according to likelihood ratio ordering. Furthermore, we apply these results when F is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.