Two-sided generalized Topp and Leone (TS-GTL) distributions

Donatella Vicari, Johan Rene Van Dorp and Samuel Kotz

Journal of Applied Statistics, 2008, vol. 35, issue 10, 1115-1129

Abstract: Over 50 years ago, in a 1955 issue of JASA, a paper on a bounded continuous distribution by Topp and Leone [C.W. Topp and F.C. Leone, A family of J-shaped frequency functions, J. Am. Stat. Assoc. 50(269) (1955), pp. 209-219] appeared (the subject was dormant for over 40 years but recently the family was resurrected). Here, we shall investigate the so-called Two-Sided Generalized Topp and Leone (TS-GTL) distributions. This family of distributions is constructed by extending the Generalized Two-Sided Power (GTSP) family to a new two-sided framework of distributions, where the first (second) branch arises from the distribution of the largest (smallest) order statistic. The TS-GTL distribution is generated from this framework by sampling from a slope (reflected slope) distribution for the first (second) branch. The resulting five-parameter TS-GTL family of distributions turns out to be flexible, encompassing the uniform, triangular, GTSP and two-sided slope distributions into a single family. In addition, the probability density functions may have bimodal shapes or admitting shapes with a jump discontinuity at the 'threshold' parameter. We will discuss some properties of the TS-GTL family and describe a maximum likelihood estimation (MLE) procedure. A numerical example of the MLE procedure is provided by means of a bimodal Galaxy M87 data set concerning V-I color indices of 80 globular clusters. A comparison with a Gaussian mixture fit is presented.

Keywords: bimodal distribution; maximum likelihood estimation; order statistics (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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DOI: 10.1080/02664760802230583

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