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Dependence Among Order Statistics for Time-transformed Exponential Models
Probability in the Engineering and Informational Sciences
  • Subhash C. Kochar, Portland State University
  • Fabio Spizzichino, University of Rome
Document Type
Pre-Print
Publication Date
1-1-2023
Subjects
  • Probability and statistics
Abstract

Let (X1, . . . ,Xn) be a random vector distributed according to a time-transformed exponential model. This is a special class of exchangeable models, which, in particular, includes multivariate distributions with Schur-constant survival functions and with identical marginals. Let for 1 ≤ i ≤ n, Xi:n denote the corresponding ith order statistic. We consider the problem of comparing the strength of dependence between any pair of Xi’s with that of the corresponding order statistics. It is proved that for m = 2, . . . , n, the dependence of X2:m on X1:m is more than that of X2 on X1 according to more stochastic increasingness (positive monotone regression) order, which in turn implies that (X1:m,X2:m) is more concordant than (X1,X2). It will be interesting to examine whether these results can be extended to other exchangeable models.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Persistent Identifier
https://archives.pdx.edu/ds/psu/40795
Citation Information
Subhash C. Kochar and Fabio Spizzichino. "Dependence Among Order Statistics for Time-transformed Exponential Models" Probability in the Engineering and Informational Sciences (2023)
Available at: http://works.bepress.com/subhash_kochar/60/