Sine π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-power odd-G family of distributions with applications

Abstract

This paper investigates a novel category of probability distributions and a specific member within this category. We have formulated a new family of trigonometric distributions by utilizing the odds ratio derived from the distribution function of a base distribution. This newly devised distribution family termed the “Sine pie-power odd-G family” of distributions, is constructed through a transformation involving the sine function. The paper presents an overview of the fundamental characteristics inherent to this proposed distribution family. Using the Weibull distribution as a base reference, we have introduced a member belonging to the proposed distribution family. This member demonstrates various hazard functions such as j, reverse-j, increasing, decreasing, or bathtub shapes. The paper examines essential statistical attributes of this newly introduced distribution. The estimation of the distribution’s parameters is carried out via the maximum likelihood estimation method. The accuracy of the parameter estimation procedure is validated through Monte Carlo simulations. The outcomes of these simulations reveal a reduction in biases and mean square errors as sample sizes increase, even for small samples. Two sets of real-engineering data are considered to demonstrate the proposed distribution’s applicability. The performance of the suggested distribution is evaluated using some model selection criteria and goodness-of-fit test statistics. Empirical evidence from these evaluations substantiates that the proposed model outperforms six existing models.