Moments of some J-shaped distributions |
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| Authors: | Saralees Nadarajah Samuel Kotz |
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| Institution: | 1. Department of Mathematics , University of South Florida , Tampa , Florida , USA;2. Department of Engineering Management and Systems Engineering , The George Washington University , Washington , USA |
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| Abstract: | This paper concerns a family of univariate distributions suggested by Topp & Leone in 1955. Topp & Leone provided no motivation for this new family and by way of properties they derived only the first four integer-order moments, i.e. E(Xn) for n=1, r 2, r 3, r 4 . In this paper we provide a motivation for the family of distributions and derive explicit algebraic expressions for: (1) hazard rate function; (2) E(Xn) when n ± 1 is any integer; (3) E(Xn) for n=1, r 2, r … r , r 10 , and (4) E{X-E(X)} n] , n=2, r 3, r 4 . We also give an expression for the characteristic function and discuss issues on estimation and simulation. The main calculations of this paper use properties of the Gauss hypergeometric function. |
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