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In this paper, an expression for computing the Pearson’s correlation coefficient between the random upper record value,and the random number of observations,is obtained. Also derived are theoretical results for the joint bivariate probability function (pf) ofandtheir marginal pf, and an alternate expression (to the correlation coefficient) measuring their dependence, where the support fordepends on an unknown threshold and an terminal parameter. Furthermore, some distributional properties are presented. The results are new to the literature on upper record value and interesting from the practicality and usefulness of upper record values. Analogous results for the lower record value are made available in another article. The concept and the derived expressions are illustrated using the recorded radiation levels in a nuclear disaster on March 2011 at Fukushima, Japan.

Does how long observing correlate with upper record value? Fukushima nuclear disaster’s radiation levels are illustrated