Modified alpha power transformed Topp-Leone family of distributions with applications and regression

Abstract

The Modified Alpha Power Transformed Topp-Leone Family of Distributions represents a novel modification of the Topp-Leone family of distributions, offering enhanced flexibility and versatility in modeling a wide range of lifetime data sets. This new family of distributions maintains a closed-form cumulative distribution function, presenting ease in statistical modeling and analysis. The Burr XII and Weibull distributions were used as special cases to ascertain the flexibility and applicability of this proposed family. Six estimation methods were utilized to estimate the parameters of the new family. The findings of the study give credence to the modeling abilities of the proposed family when used in the modification of other classical distributions. Using the proposed model, a regression model called log-modified alpha power transformed Topp-Leone Weibull distribution is proposed.