Simulating phenomena with exponentiated trigonometric distributions: a comparative study of estimation methods and real-world applications

Abstract

AbstractRecent research has highlighted the statistical significance and usefulness of trigonometric distribution models for simulating a variety of phenomena. A new set of distributions generated by exponentiated cosine and tangent functions has been introduced. Consequently, two families of distributions called the exponentiated cosine and tan Stacy distributions are derived. Some vital statistical and reliability characteristics are studied. The finite sample characteristics of parameter estimations are compared to the exponentiated cosine and tan distribution generated by four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Cramer–von Mises. The methodologies are evaluated using simulation studies. Finally, the practical applications of the proposed trigonometric versions of the Stacy model are examined and applied on two lifetime reliability engineering datasets and another lifetime medical dataset concerning bladder cancer data. These real applications serve to highlight the effectiveness and adaptability of this innovative families within the respective fields compared with other lifetime well-known distribution models.