Sine modified-kies generalized family of distributions: properties & applications

Abstract In this study, we introduce a new trigonometric-based family of distributions, called the Sine Modified-Kies Generalized family (SMKG) of distributions, designed to handle skewed and heavy-tailed data. For the proposed family, we derived statistical properties, including the quantile function, hazard function, moments, and order statistics, which are thoroughly analyzed and discussed. A special case of this family, obtained by selecting the Lomax distribution as the baseline distribution and named it the Sine Modified-Kies Lomax (SMKL) distribution. For this distribution, we derive statistical properties and illustrate various shapes of the probability density function such as left-skewed, right-skewed, and symmetric shapes, while the hazard function displays diverse behaviors such as increasing, decreasing, and bathtub-shaped curves. Parameters are estimated using the maximum likelihood method and a simulation study is conducted to assess the performance of the estimators. The flexibility and robustness of the SMKL model is achieved through its superior fit to the three real-world datasets. These results underscore its potential as a valuable tool for modeling complex lifetime phenomena, particularly in physical systems where reliability and failure behavior are of interest.