A note on the ℒ-class of life distributions

Author:

Klar B.

Abstract

This paper first recalls some stochastic orderings useful for studying the ℒ-class and the Laplace order in general. We use these orders to show that the higher moments of an ℒ-class distribution need not exist. Using simple sufficient conditions for the Laplace ordering, we give examples of distributions in the ℒ- and ℒα-classes. Moreover, we present explicit sharp bounds on the survival function of a distribution belonging to the ℒ-class of life distributions. The results reveal that the ℒ-class should not be seen as a more comprehensive class of ageing distributions but rather as a large class of life distributions on its own.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A test of exponentiality against ℳ alternatives;Journal of Nonparametric Statistics;2019-07-03

2. Shapes of Hazard Functions and Lifetime Distributions;Texts in Applied Mathematics;2019

3. A new test for exponentiality against HNBUE alternatives;Communications in Statistics - Theory and Methods;2018-12-29

4. On an ageing class based on the moment generating function order;Journal of Applied Probability;2018-06

5. A test for detecting Laplace order dominance and related Bahadur efficiency issues;Statistical Papers;2017-03-31

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