A discrete distribution including the Poisson. Issue 8 (17th April 2016)

• Record Type: Journal Article
• Authors: Déniz, Emilio Gómez; Sarabia, José María
• Is Part Of: Communications in statistics. Volume 45:Issue 8(2016)
• Page Start: 2311
• Page End: 2322
• Publication Date: 2016-04-17
• Subjects: Failure rate -- Fitting -- Index of dispersion -- Poisson distribution.; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.879896
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: This article presents a new generalization of the Poisson distribution, with the parameters α > 0 and θ > 0, using the Marshall and Olkin (1997 ) scheme and adding a parameter to the classical Poisson distribution. The particular case of α = 1 gives the Poisson distribution. The new distribution is unimodal and has a failure rate that monotonically increases or decreases depending on the value of the parameter α. After reviewing some of the properties of this distribution, we investigated the question of parameter estimation. Expected frequencies were calculated for two data sets, one with an index of dispersion larger than one and the other with an index of dispersion smaller than one. In both cases the distribution provided a very satisfactory fit.