New Insights and Applications of Survival Cumulative Sharma–Taneja–Mittal Entropy

Abstract

The literature has introduced several extensions of Shannon function entropy, including the Sharma–Taneja–Mittal entropy and its extensions. This paper presents new findings related to the survival cumulative Sharma–Taneja–Mittal entropy measure, including bounds, convergence, equivalent expressions, normalized survival cumulative Sharma–Taneja–Mittal entropy, its relationship with differential entropy, stochastic comparisons, and the excess wealth transform involving this measure. Additionally, the paper addresses the challenge of estimating the survival cumulative Sharma–Taneja–Mittal entropy using the empirical cumulative distribution function. Moreover, this entropy measure is estimated using two distinct empirical estimators of the cumulative distribution function. In addition, the measure is used to assess test uniformity, yielding an approximation of the distribution of the test statistic as well as the derivation of the limit distribution. The study also contains a simulation study to evaluate the power of the suggested test with other uniformity tests, and it covers the percentage points and power versus seven different distributions for this test statistic.