Glaser’s function and stochastic orders for mixture distributions
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 5 September 2016
Abstract
Purpose
The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented.
Design/methodology/approach
First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components.
Findings
The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order.
Originality/value
Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.
Keywords
Citation
Jarrahiferiz, J., Mohtashami Borzadaran, G.R. and Rezaei Roknabadi, A.H. (2016), "Glaser’s function and stochastic orders for mixture distributions", International Journal of Quality & Reliability Management, Vol. 33 No. 8, pp. 1230-1238. https://doi.org/10.1108/IJQRM-04-2013-0072
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited