Existence conditions and properties for the generalized Euler family of distributions
type: Item
instance of: scholarly article
title: Existence conditions and properties for the generalized Euler family of distributions
zbMATH Open document ID: 0994.60015
DOI: 10.1016/S0378-3758(01)00164-1
author: Adrienne W. Kemp
published in: Journal of Statistical Planning and Inference
publication date: 2002-05-15T00:00:00Z
review text: The paper investigates a generalized Euler family of distributions and obtains the following significant results: (1) Existence conditions for the probability mass function and the probability generating function of the corresponding generalized Euler family of distributions. (2) Identification of the obtained conditions with those corresponding to various distributions already existing in the literature. (3) For the considered class of distributions, the author examines several important properties using the methods enclosed in the valuable approach of \textit{P. L. Gupta}, \textit{R. C. Gupta} and \textit{R. C. Tripathi} [ibid. 65, No. 2, 255-268 (1997; Zbl 0908.62099)], showing that these properties depend greatly on the parameter constraints: logconcavity, logconvexity, failure rate behaviour, infinite divisibility, strong unimodality, over- and underdispersion.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 1741597
zbMATH Keywords: Euler distribution
zbMATH Keywords: Heine distribution
zbMATH Keywords: inverse absorption distribution
zbMATH Keywords: \(q\)-binomial distribution
zbMATH Keywords: logconvexity
zbMATH Keywords: logconcavity
zbMATH Keywords: IFR
zbMATH Keywords: DFR
zbMATH Keywords: overdispersion
zbMATH Keywords: infinite divisibility
zbMATH Keywords: strong unimodality
zbMATH Keywords: underdispersion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1741597