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On the Convolution of Heterogeneous Bernoulli Random Variables

Part of:Distribution theory - ProbabilitySurvival analysis and censored dataNonparametric inferenceSampling theory, sample surveys

Published online by Cambridge University Press:  14 July 2016

Maochao Xu and
N. Balakrishnan
Maochao Xu*
Affiliation:
Illinois State University
N. Balakrishnan*
Affiliation:
McMaster University
*
∗ Postal address: Department of Mathematics, Illinois State University, Normal, IL, USA. Email address: mxu2@ilstu.edu
∗∗ Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada.
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Abstract

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In this paper, some ordering properties of convolutions of heterogeneous Bernoulli random variables are discussed. It is shown that, under some suitable conditions, the likelihood ratio order and the reversed hazard rate order hold between convolutions of two heterogeneous Bernoulli sequences. The results established here extend and strengthen the previous results of Pledger and Proschan (1971) and Boland, Singh and Cukic (2002).

Keywords

Bernoulliheterogeneous variablelikelihood ratio ordermajorizationreversed hazard rate order

MSC classification

Secondary:60E15: Inequalities; stochastic orderings62N05: Reliability and life testing62G30: Order statistics; empirical distribution functions62D05: Sampling theory, sample surveys

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011, pp. 877 - 884
Copyright
Copyright © Applied Probability Trust 2011 

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