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

• Published in: Revstat Vol. 14; no. 3
• Main Authors: Jalil Jarrahiferiz, GholamReza Mohtashami Borzadaran, Abdolhamid Rezaei Roknabadi
• Format: Journal Article
• Language: English
• Published: Instituto Nacional de Estatística | Statistics Portugal 01.06.2016
• Subjects: dual weak likelihood ratio ordering; hazard rate order; likelihood ratio order; shock models; totally positive of order 2 ( TP2)
• ISSN: 1645-6726; 2183-0371
• DOI: 10.57805/revstat.v14i3.188

One notion of stochastic comparisons of non-negative random variables based on ratios of nth 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.