Compounding of distributions: a survey and new generalized classes

Muhammad H Tahir () and Gauss M. Cordeiro ()
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Muhammad H Tahir: The Islamia University of Bahawalpur
Gauss M. Cordeiro: Universidade Federal de Pernambuco

Journal of Statistical Distributions and Applications, 2016, vol. 3, issue 1, 1-35

Abstract: Abstract Generalizing distributions is an old practice and has ever been considered as precious as many other practical problems in statistics. It simply started with defining different mathematical functional forms, and then induction of location, scale or inequality parameters. The generalization through induction of shape parameter(s) started in 1997, and the last two decades were full of such practices. But to cope with the complex situations under series and parallel structures, the art of mixing discrete and continuous started in 1998. In this article, we present a survey on compounding univariate distributions, their extensions and classes. We review several available compound classes and propose some new ones. The recent trends in the construction of generalized and compounding classes are discussed, and the need for future works are addressed.

Keywords: Compound G-classes; generalized classes; G-geometric class; G-Poisson class; power series class; Primary 60E05; secondary 62N05; 62F10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (14)

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DOI: 10.1186/s40488-016-0052-1

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