Weibull-Exponential Pareto Distribution: Order Statistics, Properties and Application to Nigeria Covid-19 Active Cases


Abstract


The Weibull Exponential Pareto (WEP) distribution is a convolution of the Weibull and Exponential Pareto distributions using Weibull-X technique. The distribution generalizes some existing distributions in the literatures. This article presents a new dimension to the study of convoluted distribution by exploring the statistical tools and properties of order statistics from the WEP distribution. The study derived distribution of sample median; the explicit expressions for the distributions of order statistics, extreme order statistics, joint density of two order statistics X(r:n) and X(s:n) for 0 < r < s < n; the sample range statistics Rn = X(n:n) −X(1:n) and their respective moments for WEP distribution was derived. The study demonstrated the use of beta-G procedure for deriving distributions of the extreme order statistics. The mean and variances of order statistics X(r:n) and the minimum order statistics X(1:n) and the mean value of the sample range Rn were derived. The recurrence relation for the moment of order statistics from WEP distribution was presented. Application of the WEP distribution to Covid-19 data analyzed using the R-software reveals it has adequate modeling capacity for the data. The goodness-of-fit estimates of parameters from the computational results was used to predict the expected occurrences for the maximum and minimum number of Covid-19 active cases of patients on admission for any sample of size n. Some numerical computations for the mean of order statistics of WEP distribution was tabulated for a random sample of size n = 4.

Keywords: Weibull Exponential Pareto Distribution; Order Statistics; Sample Range Statistic; Extreme Order Statistics; Covid-19 Active Cases; Moment of Order Statistics.

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