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On the general class of two-sided power distribution. (English) Zbl 1065.60011
Summary: J. R. van Dorp and S. Kotz [ibid. 32, 1703–1723 (2003; Zbl 1171.60315)] introduced a general class of two-sided power distributions. We provide several examples of this distribution by considering a nonnegative, nondecreasing differentiable function \(g\) on [0, 1] satisfying \(g(1)-g(0)=1\). For the considered distributions the maximum likelihood estimation and moment estimation of parameters are obtained. Moments, moment generating functions, and relative entropy are also derived.

MSC:
60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
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References:
[1] Johnson D., The Statistician 46 pp 387– (1997)
[2] Johnson N. L., The Statistician 48 pp 179– (1999)
[3] DOI: 10.1016/S0304-4076(01)00111-7 · Zbl 1051.62006 · doi:10.1016/S0304-4076(01)00111-7
[4] Van Dorp J. R., The Statistician 51 pp 1– (2002)
[5] DOI: 10.1198/000313002317572745 · Zbl 1182.62017 · doi:10.1198/000313002317572745
[6] DOI: 10.1081/STA-120022704 · Zbl 1171.60315 · doi:10.1081/STA-120022704
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