The Alpha Power Topp–Leone Dagum Distribution: Theory and Applications

This article introduces a new flexible distribution, called the alpha power Topp–Leone Dagum (APTLDa) distribution, which extends the classical Dagum model by combining the Topp–Leone generator with the alpha power transformation (APT). The proposed distribution is capable of modeling data with symmetrical and asymmetrical shapes for the probability density and hazard rate functions. This makes it suitable for lifetime and reliability data analysis. Several important statistical properties of the new distribution are derived, including the quantile function, moments, entropy measures, order statistics, and reliability-related functions. Parameter estimation is carried out using the maximum likelihood method, and the performance of the estimators is examined through an extensive simulation study under different sample sizes and parameter settings. The simulation results demonstrate the consistency and good finite-sample behavior of the estimators. The practical usefulness of the proposed distribution is illustrated through applications to two real datasets, where its performance is compared with several competing models. The results show that the APTLDa distribution provides a flexible and effective alternative for modeling lifetime data.