Analyzing Order Statistics of Non-Identically Distributed Shifted Exponential Variables in Numerical Data

In this study, we analyze the order statistics (OS) arising from independent, non-identically distributed (INID) Shifted Exponential (SH-E) random variables. We deduce the moments of the rth order statistic, provide graphical representations of the probability density function (PDF) and cumulative distribution function (CDF) and present numerical examples, including cases where n = 3. This research offers insights into the distributional properties of SH-E variables and their practical applications in numerical data analysis.