Abstract
Nashaat [25] introduced the powered inverse Rayleigh (PIR) distribution. It provides a better fit other than (inverse Rayleigh, Rayleigh, and Weibull) distributions. The moments of order statistics and recurrence relations for the single and double moments have been established. The computation of the means and variances are enumerated. These computations can be trulyinteresting and applied in numerous domains of study. Moreover, cumulative entropy (C.E.) and actuarial measures (A.M.) are also calculated to address the uncertainty in portfolio optimization. The usages of C. E. and A.M. are widespread in many real-word applications specifically in physical sciences and insurance science.
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