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ORDERING PROPERTIES OF SPACINGS FROM HETEROGENEOUS GEOMETRIC SAMPLES

Published online by Cambridge University Press:  10 May 2017

Weiyong Ding ,
Yiying Zhang  and
Peng Zhao
Weiyong Ding
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
Yiying Zhang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China E-mail: zhaop@jsnu.edu.cn
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Abstract

In the reliability context, the geometric distribution is a natural choice to model the lifetimes of some equipment and components when they are measured by the number of completed cycles of operation or strokes, or in case of periodic monitoring of continuous data. This paper aims at investigating how the heterogeneity among the parameters affects some characteristics such as the distribution and hazard rate functions of spacings arising from independent heterogeneous geometric random variables. First, refined representations of the distribution functions are provided for both the second spacing and sample range from heterogeneous geometric sample. Second, stochastic comparisons are carried out on the second spacings and sample ranges for two sets of independent and heterogeneous geometric random variables in the sense of the usual stochastic and hazard rate orderings. The results established here not only fill the gap on the study of stochastic properties of spacings from heterogeneous geometric samples, but also are expected to be applied in the fields of statistics and reliability.

Keywords

geometric distributionhazard rate orderingmajorizationsample rangesecond spacingusual stochastic ordering
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 2 , April 2018 , pp. 306 - 322
Copyright
Copyright © Cambridge University Press 2017 

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