A New Sine-Based Probabilistic Approach: Theory and Monte Carlo Simulation with Reliability Application

Abstract

Data modeling is a very crucial stage for decision making in applied sectors. Probability distributions are considered important tools for decision making. So far, numerous probability distributions have been developed and implemented. Most of these distributions are developed by introducing from one to eight additional parameters. Sometimes, the addition of new parameters leads to re-parameterization problems. To avoid such issues, we introduce a novel probabilistic approach. The proposed approach may be termed as a new weighted sine-$G$ method. The beauty and key advantage of the new weighted sine-$G$ method are that it has no additional parameters. Through using the new weighted sine-$G$ method, a new weighted sine-Weibull distribution is introduced, which is a modification of the Weibull distribution. The estimators of the new model are also derived. Furthermore, a simulation study is carried out to evaluate the estimators of the new weighted sine-Weibull distribution. Finally, a practical application from the reliability sector is considered to evaluate the new weighted sine-Weibull distribution. Based on certain decision tools, it is observed that the proposed model is the best competing distribution for applying it in the reliability sector.