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

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  • Donatella Vicari
  • Johan Rene Van Dorp
  • Samuel Kotz
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    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.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 35 (2008)
    Issue (Month): 10 ()
    Pages: 1115-1129

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    Handle: RePEc:taf:japsta:v:35:y:2008:i:10:p:1115-1129

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    Related research

    Keywords: bimodal distribution; maximum likelihood estimation; order statistics;

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    Cited by:
    1. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, vol. 53(1), pages 117-131, February.

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