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A Unified Approach to Ordering Comparison of GPS Distributions with their Mixtures
Authors:Mansour Aghababaei Jazi  Somayyeh Abbasi
Institution:1. Department of Statistics , University of Isfahan , Isfahan , Iran;2. Naghshejahan Institute of Higher Education , Isfahan , Iran
Abstract:Recently, several authors have been concerned with ordering comparison of known distributions of the family of generalized power series (GPS) distributions with their mixtures in various senses. In this article, we shall employ a unified approach and obtain similar results, more generally, for all members of the class of the GPS distributions. Some of the previous findings of Misra et al. (2003 Misra , N. , Singh , H. , Harner , E. J. ( 2003 ). Stochastic comparisons of Poisson and binomial random variables with their mixtures . Statist. Probab. Lett. 65 : 279290 .Crossref], Web of Science ®] Google Scholar]), Alamatsaz and Abbasi (2008 Alamatsaz , M. H. , Abbasi , S. ( 2008 ). Ordering comparison of negative binomial random variables with their mixtures . Statist. Probab. Lett. 78 : 22342239 . Google Scholar]), and Aghababaei Jazi and Alamatsaz (2010 Aghababaei Jazi , M. , Alamatsaz , M. H. ( 2010 ). Ordering comparison of logarithmic series random variables with their mixtures . Commun. Statist. Theor. Meth. 39 : 32523263 .Taylor & Francis Online], Web of Science ®] Google Scholar]) in this connection, then, follow as corollaries. Further, we have derived some more ordering comparison results.
Keywords:Convex ordering  Generalized power series (GPS) distributions  Hazard rate ordering  Likelihood ratio ordering  Mixtures  Simple stochastic ordering  Uniformly more variable ordering
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