Properties of N-Laplace Transform Ratio Order and L(N)-Class of Life Distributions

Abstract

One notion of stochastic comparisons of non-negative random variables based on ratios of n^th derivative of Laplace transforms (n-Laplace transform order or shortly ≤_n-Lt-r order) is introduced by Mulero et al. (2010). In addition, they studied some of its applications in frailty models. In this paper, we have focused on some further properties of this order. In particular, we have shown that ≤_n-Lt-r order implies dual weak likelihood ratio order (≤_DWLR order). Moreover, ≤_n-Lt-r order, under certain circumstances, implies likelihood ratio order (≤_lr order). Finally, the L⁽ⁿ⁾ (L¯(n) )-class of life distribution is proposed and studied. This class reduces to L (L¯)-class if we take n = 0.