Some Properties of Alpha Power Gumbel Distribution

Abstract

     This paper defines and studies a new Alpha Power transformation distribution. This model is called the Alpha Power Gumbel distribution, which has shape parameters (φ) and a scale parameter (δ). Statistical functions like probability density function, cumulative distribution function, hazard function, and survival function were investigated by introducing basic properties such as quantile function, moment function, moment generating function, and entropies. To approximate the parameters of this model, the maximum likelihood estimator method was employed, simulated distribution by using mean squared error and the bias, and real-life data was applied to compare this model with other related distributions using criteria like the Akaike Information Criterion, Akaike Information Criterion Corrected, Bayesian Information Criterion, and Hannan–Quinn information criterion. As a result, the Alpha Power Gumbel distribution is more flexible than some traditional distributions.