The SAS Family of Distributions: Properties and Applications
Keywords:
Transformation technique, Topp-Leone distribution, order statistics, classical method of estimation, simulation studyAbstract
In this study, our aim is to introduce a new transformation based on the cumulative distribution function (CDF), known as the SAS-transformation, an acronym derived from the names of its developers: Shantanu, Arun and Shubham. The proposed transformation technique is illustrated using the Toppe-Leone distribution as a baseline. We computed its various statistical properties, including the survival function, hazard rate function, moments, conditional moments, quantile function, mean deviation, order statistics, entropy, stochastic ordering and identifiability. We conduct a simulation study to assess the long-term performance of the model and estimator’s under different classical estimation methods. Finally, to demonstrate the practical applicability of the proposed model, we apply it to three real datasets and assess its performance using the Akaike information criterion (AIC), Corrected Akaike information criterion (AICc), Bayesian information criterion (BIC), and log-likelihood (LL) values.
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