Moments of some J-shaped distributions
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.
Year of publication: |
2003
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Authors: | Nadarajah, Saralees ; Kotz, Samuel |
Published in: |
Journal of Applied Statistics. - Taylor & Francis Journals, ISSN 0266-4763. - Vol. 30.2003, 3, p. 311-317
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Publisher: |
Taylor & Francis Journals |
Saved in:
Online Resource
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