A novel cosine-derived probability distribution: Theory and data modeling with computer knowledge graph

It is a deep-rooted and already observed reality that probabilistic models play an important role in describing and explaining the events/situations under consideration. Focusing attention on the fundamental role and applicability of the probabilistic models, this article considers the development of a new probability model derived through the implementation of a trigonometric function. The suggested model is named as a new cosine flexible Weibull (NCF-Weibull) distribution. This model is accomplished by exploiting the cosine functional approach. Some statistical characteristics of the NCF-Weibull distribution are given. Alongside, the estimates of the NCF-Weibull model are also obtained. Besides them, a simulation study for different settings of the parameter values of the NCF-Weibull model is also provided. Through the simulation study it is evidenced that the estimators of the NCF-Weibull distribution consistently perform well in terms of stability, consistency, and efficiency. Finally, the optimality of the NCF-Weibull distribution is judged by using two applications from different sectors. Based on five evaluation criteria alongside the p-value, the NCF-Weibull distribution shows optimal performances for both data sets.