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A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution

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  • Francesca Condino

    (University of Calabria)

  • Filippo Domma

    (University of Calabria)

Abstract

In this paper we introduce a new flexible class of distributions with bounded support, called reflected Generalized Topp-Leone Power Series (rGTL-PS), obtained by compounding the reflected Generalized Topp-Leone as reported by van Dorp and Kotz (Modeling Income Distributions Using Elevated Distributions, pp. 1–25. Distribution Models Theory. World Scientific Press, Singapore, 2006) and the family of Power Series distributions. The proposed class includes, as special cases, some new distributions with limited support such as the rGTL-Logarithmic, the rGTL-Geometric, the rGTL-Poisson and rGTL-Binomial. This work is an attempt to partially fill a gap regarding the presence, in the literature, of continuous distributions with bounded support, which instead appear to be very useful in many real contexts, such as reliability. Some properties of the class, including moments, hazard rate and quantile are investigated. Moreover, the maximum likelihood estimators of the parameters are examined and the observed Fisher information matrix provided. Finally, in order to show the usefulness of the new class, two applications to real data are reported.

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  • Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    • Handle: RePEc:spr:metron:v:75:y:2017:i:1:d:10.1007_s40300-016-0095-6
    DOI: 10.1007/s40300-016-0095-6
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