New Generalized Odd Fréchet-G (NGOF-G) Family of Distribution with Statistical Properties and Applications

The distribution theory literature contains recent types of parametric distributional models that have been successfully used in the past and whose goodness of fit is sufficient only for certain datasets, suggesting further attention to accommodate a wider range of real-world datasets, for more adaptability, efficiency, and applications. This study aims to develop an extended Fréchet-G family of distributions and study their mathematical properties. The method of Alzaatreh is employed in developing a new lifetime continuous probability distribution called the new Generalized Odd Fréchet-G Family of Distribution. The developed distribution is flexible for studying positive real-life datasets. The statistical properties related to this family are obtained. The parameters of the family were estimated by using a technique of maximum likelihood. A New Generalized Odd Fréchet-Weibull model is introduced. This distribution was fitted with a set of lifetime data. A Monte Carlo simulation is applied to test the consistency of the estimated parameters of this distribution in terms of their bias and mean squared error with a comparison of M.L.E and the maximum product spacing (MPS). The findings of the Monte Carlo simulation show that the M.L.E method is the best technique for estimating the parameter of New Generalized Odd Frechet-Weibull distribution than the M.PS method. The findings of the application on the data set produce a higher flexibility than some of the competing distributions. In general, our new distributions serve as a viable alternative to other distributions available in the literature for modelling positive data.