A new probability distribution with properties and statistical analysis of the human resource and radiation data

Abstract

To assist researchers in optimally fitting practical events and strengthen the available data analysis toolkits, we propose a new distributional method constructed using a trigonometric function. Henceforth, the proposed method is based on the cosine function and referred to as a new cosine trigonometric-$G$ (NCT-$G$) function. The incorporation of the cosine function in the development of the NCT-$G$ method leads to significantly improved and optimal versions of the conventional probability distributions. By applying the NCT-$G$ method, we concentrate on a new variant of the Weibull distribution, namely, a new cosine trigonometric Weibull (NCT-Weibull) distribution. Due to the implementation of the cosine function, we promptly show that the NCT-Weibull distribution has more flexibility in terms of density and hazard functions. Some mathematical features of the NCT-Weibull distribution, notably those associated with quartiles, are computed. We derive the estimators for the new distribution. Moreover, we assess these point estimators via conducting simulation studies for various parameter values. Finally, intending to establish the fitting superiority of the NCT-Weibull distribution, we consider two data sources from the human resource and radiation science. According to certain fitting criteria, the empirical exploration indicates that the NCT-Weibull distribution demonstrates optimal performance.