Moments of some J-shaped distributions

Saralees Nadarajah and Samuel Kotz

Journal of Applied Statistics, 2003, vol. 30, issue 3, 311-317

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.

Date: 2003
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Citations: View citations in EconPapers (17)

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DOI: 10.1080/0266476022000030084

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