The Power Reduced Kies Distribution: Theory and Applications in Environmental, Insurance and Health Sciences

The adequacy of a statistical model ultimately rests on how faithfully the chosen distribution captures the structural features of the data at hand, including skewness, kurtosis, multi-modality, and the shape of the HRF. Consequently, the construction of new and more flexible distributions remains an active and consequential area of statistical research. In the same vein, this study introduces the Power Reduced Kies distribution (PRKD), a new two-parameter bounded distribution obtained through the power transformation of random variable of the Reduced Kies distribution. The inclusion of the power parameter endows the PRKD with a substantially richer variety of density shapes, including decreasing, right-skewed, left-skewed, reversed-J, and approximately symmetric forms, as well as a wider range of hazard rate behaviours, including increasing and bathtub-shaped forms, none of which can be collectively achieved by the single-parameter Reduced Kies distribution. Several important statistical properties of the PRKD are derived, including its linear representation, reliability characteristics, quantile function, moments, moment generating function, mode, and order statistics. The model parameters are estimated using the maximum likelihood and maximum product of spacings methods. A Monte Carlo simulation study is conducted to examine the finite-sample performance of the estimators under different parameter settings and sample sizes using mean estimates and mean squared errors. The results indicate that both estimators perform satisfactorily, although the maximum product of spacings method generally provides more reliable estimates for smaller sample sizes. The practical applicability of the PRKD is demonstrated using four real datasets from environmental, insurance, and health sciences. Comparative analyses with twelve competing unit distributions reveal that the PRKD provides highly competitive fits according to several model selection criteria and goodness-of-fit measures.