On the maximal correlation coefficient for the bivariate Marshall Olkin distribution
Axel B\"ucher, Torben Staud
TL;DR
This paper derives a formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution, confirming a previous conjecture and applying it to establish a variance inequality in extreme value statistics.
Contribution
It provides a proven formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution, advancing theoretical understanding in dependence measures.
Findings
Confirmed the conjectured formula for maximal correlation coefficient.
Applied the formula to prove a variance inequality in extreme value statistics.
Linked disjoint and sliding block maxima methods through the new inequality.
Abstract
We prove a formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution that was conjectured in Lin, Lai, and Govindaraju (2016, Stat. Methodol., 29:1-9). The formula is applied to obtain a new proof for a variance inequality in extreme value statistics that links the disjoint and the sliding block maxima method.
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Bayesian Methods and Mixture Models · Probability and Risk Models