A modified sine Weibull distribution with applications to finance and radiation sectors

Abstract

We present a novel approach that utilizes a familiar trigonometric function with the aim of enhancing the descriptions of real-world events. The presented method mainly relies on the sine function and is henceforth referred to as the modified sine-$G$ (MS-$G$) approach. The MS-$G$ method updates the data analysis tools by providing a more precise representation of practical data sets. In our case study, we utilize the MS-$G$ method on the Weibull distribution leading to a new model termed the modified sine-Weibull (MS-Weibull) distribution. We investigate different mathematical characteristics of the MS-Weibull distribution, with particular emphasis on its quantile function, which is crucial for generating random variates and defining quartiles as well as percentiles We also carry out the mathematical derivations of point estimators for the MS-Weibull distribution. The derived estimators are further evaluated through simulation studies under various parameter values. To validate the MS-Weibull distribution, we analyze two data sets, taken from the finance and radiation fields. Our investigations using numerical and visual methods show that the MS-Weibull distribution repeatedly offers the best results based on specific criteria for assessing the goodness of fit of the model to the data.