A new family of alpha power-G using cosine function with applications and regression modeling

This paper discusses a novel technique to creating distribution families by combining the transformation of alpha power and the cosine function. The proposed technique have been named the cosine alpha power-generated family. The Weibull distribution is employed to produce a distinctive model for the cosine alpha power generated family, the specific model is called the cosine alpha power-Weibull (CAP-W). The distribution statistical characteristics are investigated, involving quantiles, Rényi entropies, and order statistics. The CAP-W has a density function that is right-skewed, symmetrical, and decreases continuously, along with J-shape, upside down bathtub, increasing and decreasing hazard rate function. Various methods of estimation-maximum likelihood, ordinary least-squares, weighted least-squares, and cramér-von mises were utilized to estimate the distribution parameters, and a simulation study is carried out to examine their performance. Furthermore, the efficiency of the provided distribution is demonstrated by four real data sets. Ultimately, the log cosine alpha power Weibull regression model is constructed and examined with a real dataset.