Conditional properties of a random sample given an order statistic

Jafar Ahmadi () and H. N. Nagaraja ()
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Jafar Ahmadi: Ferdowsi University of Mashhad
H. N. Nagaraja: The Ohio State University

Statistical Papers, 2020, vol. 61, issue 5, No 9, 1996 pages

Abstract: Abstract This paper deals with the conditional properties of unordered observations in a random sample given the ith order statistic of the same sample. A characterization of symmetric distribution is given based on the properties of conditional moments. It is proved that the joint distribution has negative quadrant dependence structure and an exact expression for the Pearson correlation coefficient is given. Stochastic ordering results are obtained and it is shown that some orderings are inherited by the conditional distribution of the sample values. The results are useful in studying the properties of component lifetimes of a system with n components given the ith failure time and associated repair costs.

Keywords: k-Out-of-n system; Moment generating function; Order statistics; Quadrant dependence; Stochastic orders; 62G30; 60E15; 62E1; 62H20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-018-1016-y

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