A Unified Approach to Ordering Comparison of GPS Distributions with their Mixtures |
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Authors: | Mansour Aghababaei Jazi Somayyeh Abbasi |
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Institution: | 1. Department of Statistics , University of Isfahan , Isfahan , Iran;2. Naghshejahan Institute of Higher Education , Isfahan , Iran |
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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 : 279 – 290 .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 : 2234 – 2239 . 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 : 3252 – 3263 .Taylor & Francis Online], Web of Science ®] , Google Scholar]) in this connection, then, follow as corollaries. Further, we have derived some more ordering comparison results. |
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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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