New results on comparisons of parallel systems with heterogeneous gamma components
type: Item
instance of: scholarly article
title: New results on comparisons of parallel systems with heterogeneous gamma components
zbMATH Open document ID: 1221.60025
author: Peng Zhao
author: Narayanaswamy Balakrishnan
published in: Statistics \& Probability Letters
publication date: 2011-01-14T00:00:00Z
review text: Let \(X_1,X_2\) be two independent gamma random variables with \(X_i\) having the shape parameter \(r>0\) and the scale parameter \(\lambda_i\), \(i=1,2\). Let \(X_1^*,X_2^*\) be another pair of independent gamma random variables with \(X_i^*\) having the shape parameter \(r>0\) and the scale parameter \(\lambda_i^*\), \(i=1,2\). The authors find conditions on the four parameters \(\lambda_1,\lambda_2,\lambda_1^*,\lambda_2^*\) such that \(\max\{X_1,X_2\}\) and \(\max\{X_1^*,X_2^*\}\) are ordered with respect to the dispersive stochastic order. They also find two other sets of conditions on \(\lambda_1,\lambda_2,\lambda_1^*,\lambda_2^*\) such that \(\max\{X_1,X_2\}\) and \(\max\{X_1^*,X_2^*\}\) are ordered with respect to the star stochastic order.
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 5836631
zbMATH Keywords: dispersive order
zbMATH Keywords: star order
zbMATH Keywords: majorization
zbMATH Keywords: \(p\)-larger order
zbMATH Keywords: parallel system
reviewed by: Moshe Shaked
MaRDI profile type: Publication
full work available at URL: j.spl.2010.09.016
OpenAlex ID: W2025280246
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DOI: 10.1016/J.SPL.2010.09.016
description: scientific article; zbMATH DE number 5836631