Alpha Power Harris-G Family of Distributions: Properties and Application to Burr XII Distribution

This study introduces a new family of probability distributions, termed the alpha power Harris-generalized (APHG) family. The generator arises by incorporating two shape parameters from the Harris-G framework into the alpha power transformation, resulting in a more flexible class for modelling survival and reliability data. A special member of this family, obtained using the two-parameter Burr XII distribution as the baseline, is developed and examined in detail. Several analytical properties of the proposed alpha power Harris Burr XII (APHBXII) model are derived, which include closed-form expressions for its moments, mean and median deviations, Bonferroni and Lorenz curves, order statistics, and Renyi and Tsallis entropies. Parameter estimation is performed via maximum likelihood, and a Monte Carlo simulation study is carried out to assess the finite-sample performance of the estimators. In addition, three real lifetime datasets are analyzed to evaluate the empirical performance of the APHBXII distribution relative to four competing models. The results show that the five-parameter APHBXII model provides superior fit across all datasets, as supported by model-selection criteria and goodness-of-fit statistics.