Record-based transmuted Exponential Power distribution: Theory, Simulation, and Applications

In this paper, a novel distribution called record-based transmuted exponential power is proposed by using the record-based transmutation map. The suggested distribution serves as a flexible alternative to the exponential power and its modified ones, offering improved adaptability in modeling skewed or heavytailed real-life data structures. Some distributional properties such as moments, median, hazard function, R´enyi entropy, and stochastic ordering are examined in detail. In point estimation, nine different estimators, namely maximum likelihood, least squares, weighted least squares, Anderson-Darling and right tail Anderson Darling, Cram´er-von Mises, maximum product spacings, minimum spacing absolute distance and minimum spacing absolute log-distance estimators are used to estimate the parameters of proposed distribution. Then, a comprehensive Monte-Carlo simulation study is designed to compare these estimators in terms of estimation procedure. Among the nine estimation methods considered, the minimum spacing absolute distance estimator consistently yielded the lowest mean squared error across various sample sizes and parameter settings. Three practical data examples are provided to assess the fits of suggested model as well as its competitor ones. Three real-world data examples are considered assess both the potential of the introduced model for modeling real-life data and its superiority over competing distributions, the main one being exponential power. Based on goodness-of-fit measures such as −2 log ℓ, Kolmogorov-Smirnov statistics, Anderson-Darling statistics, Cramer-von-Mises statistics and their p-values, the RBTEP distribution outperformed classical distributions including exponential power, Weibull, transmuted Weibull, transmuted record type Weibull, and transmuted Lindley in modeling the failure time, aircraft and recidivism time datasets.