Abstract
In this paper, closed form expressions for the moments of the truncated Pareto order statistics are obtained by using conditional distribution. We also derive some results for the moments which will be useful for moment computations based on ordered data.
Highlights
Order statistics and their moments have assumed considerable interest in recent years
There is a vast literature on both theory and application of the moments of order statistics
Childs and Balakrishnan (1998) generalized the I.I.D. results for the Pareto and doubly-truncated Pareto models established by Balakrishnan and Joshi (1982)
Summary
Order statistics and their moments have assumed considerable interest in recent years. Joshi and Balakrishnan (1982) obtained several recurrence relations and identities for product moments of order statistics in a random sample of size n from an arbitrary continuous distribution. Balakrishnan and Joshi (1982) established independent and identically distributed results for the Pareto and doubly-truncated Pareto models, at the same time these results allow us to evaluate all the single and product moments of order statistics. Ahmad (2001) derived some general recurrence relations satisfied by single and product moments of order statistics from doubly truncated continuous distributions. Afify (2006) derived some recurrence relations of single and product moments of order statistics from identical Pareto distribution and estimated the parameters of the first order statistics and the mean, variance and the coefficient of variation were computed. We consider Pareto distribution since it has a wide use in economic and finance
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