Journal of the Iranian Statistical Society
Stochastic and Dependence Comparisons Between Extreme Order Statistics in the Case of Proportional Reversed Hazard Model
Authors
Abstract
Independent random
variables $Y_{1},ldots ,Y_{n}$ belongs to the
proportional reversed hazard rate (PRHR) model with
proportionality parameters $lambda_1,...,lambda_n$, if
$Y_{k}sim G^{lambda _{k}}(x)$, for $k=1,...,n$, where $G$ is an
absolutely continuous distribution function. In this paper we compare
the smallest order
statistics, the sample ranges and the ratios of the smallest and
largest order statistics of two sets of independent random
variables belonging to PRHR model, in the sense of (reversed) hazard
rate order, likelihood ratio order and dispersive order, when the
variables in one set have proportionality parameters
$lambda_1,...,lambda_n$ and the variables in the other set are
independent and identically distributed with common parameter
$overline{lambda}=sum_{k=1}^{n}lambda_k/n$. We also compare
the relative degree of dependence between the smallest and the largest
order statistics of these samples whit respect to the monotone
regression dependence order.
Keywords
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Volume 10, Issue 1
March 2011Pages 29-43
- Receive Date: 23 July 2022
- Revise Date: 20 May 2024
- Accept Date: 23 July 2022