On the Exponentiated Generalized Alpha Power Transformation Technique and Associated Inference

A new technique for constructing families of distributions, called the exponentiated generalized alpha power transformation-G (EGAPT-G), is proposed. Our new method adds two additional shape parameters and allows one to choose any baseline distribution, which makes it significant. We discuss some useful statistical properties of the EGAPT-G such as linear representation of its probability density function (PDF), PDF of its order statistics, moments, residual life functions, and Rényi entropy. Furthermore, analytical shapes of the PDFs and hazard rate functions of some special models are determined. The model parameters of the EGAPT-G are estimated using several estimation methods. A simulation study is also conducted to assess the performance of the discussed estimation methods, and it was notable that some methods show inconsistency in parameter estimation. Finally, an example of the EGAPT-G called the exponentiated generalized alpha power transformation log-logistic (EGAPT-LLoG) is applied to two biomedical datasets to prove the usefulness of the EGAPT-G. Actually, the four-parameter EGAPT-LLoG performs better than the four-parameter exponentiated generalized logarithmic, four-parameter exponentiated power Lindley Poisson, and four-parameter generalized Gompertz-Poisson. The EGAPT-LLoG also performs better than the standard distributions such as the Burr-XII, Gumbel, and Weibull models. The performance comparison was done using some well-known goodness-of-fit (GoF) statistics, and the model with the lowest GoF and highest p value was considered better. Some empirical analysis was investigated to show how well the EGAPT-LLoG fits the datasets.