Probability in the Engineering and Informational Sciences
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. 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 in particular 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:mº is more concordant than X1, X2. It will be interesting to examine whether these results can be extended to other exchangeable models.
Copyright (c) 2023 The Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
Locate the Document
Kochar, S., & Spizzichino, F. L. (2023). Dependence among order statistics for time-transformed exponential models. Probability in the Engineering and Informational Sciences, 1-16.