Cosine Weibull Family of Distributions: Properties, Simulation, and Applications to Medical Data

Based on the motivation of introducing parsimonious models for efficient analysis of real data, research works of recent times have adopted the use of trigonometric functions in developing new generalized groups of models in the area of distribution theory. As an alternative analytical tool, the cosine Weibull‐generated set of models is introduced in this current study as a parsimonious novel set of generalized models for the efficient modeling of medical data. The quantile function and moments made up the structural characterization of the newly introduced group of generalized models. Detailed derived expressions of other structural characteristics including identifiability were explicitly presented. Five specialized distributions were generated from the generated family of distributions and established to have very efficient capabilities of modeling both unimodal and bimodal datasets. Other useful properties such as J‐shapes and reversed J‐shapes were exhibited by the density functions of the specialized distributions. The specialized distributions were further established to have efficient capabilities in modeling different sets of data having varied complexities of failure rates. By maximizing the likelihood function, parameters of the new set of generalized models were approximated. Through simulated experimentation results, the developed class of models was established to have consistent estimators. Applications to two sets of data in medical studies were used in demonstrating the practical suitability of the newly introduced set of generalized models. Empirical applications showed that the cosine Weibull–Weibull and cosine Weibull–Lomax distributions of the new generated class of models offered a more adequate performance in fitting the data than other competitive models.