Correlation structure of the Marshall-Olkin bivariate exponential distribution

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• 作者：Gwo Dong Lin^a ; ^{gdlin@stat.sinica.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Chin-Diew Lai^b ; ^{c.lai@massey.ac.nz" class="auth_mail" title="E-mail the corresponding author} ; K. Govindaraju^b ; ^{k.govindaraju@massey.ac.nz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Marshall&ndash ; Olkin BVE distribution ; Copula ; Lifetime ; Lancaster&rsquo ; s theorem ; Pearson&rsquo ; s correlation ; Total positivity ; Maximal correlation
• 刊名：Statistical Methodology
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：29
• 期：Complete
• 页码：1-9
• 全文大小：378 K

文摘

We first review the basic properties of Marshall–Olkin bivariate exponential distribution (BVE) and then investigate its correlation structure. We provide the correct reasonings for deriving some properties of the Marshall–Olkin BVE and show that the correlation of the BVE is always smaller than that of its copula regardless of the parameters. The latter implies that the BVE does not have Lancaster’s phenomenon (any nonlinear transformation of variables decreases the correlation in absolute value). The dependence structure of the BVE is also investigated.