A new trigonometric-inspired probability distribution: A simulation study and applications in reliability and hydrology

The importance of statistical distributions in accurately representing real-world scenarios and aiding in educated decision-making is well recognized. Nonetheless, it is also true that the limitations of these distributions can hinder optimal fitting in certain situations. This awareness has led researchers to seek out improved and more optimal probability distributions. Based on factual motivation, this paper introduces a new probability distribution called the weighted sine generalized inverse Weibull (WSGI-Weibull) distribution. This model emerges from the amalgamation of the generalized inverse Weibull distribution and a sine-inspired probabilistic framework. Certain statistical properties, particularly those based on quantiles, of the newly introduced WSGI-Weibull distribution have been derived. An established estimation method is applied to calculate the point estimators of the WSGI-Weibull distribution, and subsequently, a simulation study is conducted. To highlight the benefits of the WSGI-Weibull distribution, two data sets sourced from the reliability and hydrology sectors are analyzed. The empirical fitting of the WSGI-Weibull distribution is evaluated against specific adversarial distributions, utilizing the two data sets as a basis for comparison. Utilizing specific evaluation tools, it has been noted that the WSGI-Weibull distribution delivers the best and most optimal fit for the reliability and hydrological data sets.