A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution. (English) Zbl 1383.62036
Summary: In this paper we introduce a new flexible class of distributions with bounded support, called reflected Generalized Topp-Leone Power Series (rGTL-PS) [C. W. Topp and F. C. Leone, J. Am. Stat. Assoc. 50, 209–219 (1955; Zbl 0064.13601)], obtained by compounding the reflected Generalized Topp-Leone as reported by J. R. van Dorp and S. Kotz [in: Distribution models theory. Selected papers based on the presentations at the 5th workshop of Spanish Scientific Association of Applied Economy on distribution models theory, Granada, Spain, September 2005. Hackensack, NJ: World Scientific. 1–25 (2006; Zbl 1276.91068)] 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.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 60E05 | Probability distributions: general theory |
| 62N05 | Reliability and life testing |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
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