Kpangay, MohamedOdongo, Leo O.Orwa, George O.2023-07-042023-07-042023Kpangay, M., Odongo, L. O., & Orwa, G. O. The Kumaraswamy-Gull Alpha Power Rayleigh Distribution: Properties and Application to HIV/AIDS Data.2581-7175http://ir-library.ku.ac.ke/handle/123456789/26062ArticleIn this paper, a new four-parameter distribution called the Kumaraswamy-Gull Alpha Power Rayleigh distribution (abbreviated as Kw-GAPR) has been proposed. Some well-known sub-models are obtained from the proposed Kw-GAPR distribution. Some statistical properties of the proposed Kw-GAPR distribution are investigated. The distribution parameters are estimated by using the method of maximum likelihood estimation. To assess the performance of the MLE estimates, a Monte Carlo simulation study was conducted. According to the results of the simulation study, as the sample size is increased, average estimates converge to the parameters’ true values and average bias, MSE, and RMSE generally decrease. The proposed Kw-GAPR distribution and its sub-models are then compared by fitting the models to an HIV/AIDS data set. From the fitted data set, a conclusion can be drawn that the proposed Kw-GAPR distribution outperforms its competing sub-models.enGull Alpha Power FamilyKumaraswamy FamilyMaximum Likelihood EstimationRayleigh distributionArticle