New alpha power transformed beta distribution with its properties and applications

Abstract

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The main purpose of this paper is to introduce a new alpha power transformed beta probability distribution that reveals interesting properties. The studuy provide a comprehensive explanation of the statistical characteristics of this innovative model. Various properties of the new distribution were derived, using the baseline beta distribution, statistical techniques, and probabilistic axioms. These include the probability density, cumulative distribution, survival function, hazard function, moments about the origin, moment generating function, and order statistics. For parameter estimation, the maximum likelihood estimation method using Newton Raphson numerical technique is employed. To evaluate the performance of our estimation method, the mean squared errors of the estimated parameters for different simulated sample sizes are used. In addition simulation studies of the new distribution are conducted to demonstrate the behavior of the probability model. To demonstrate the practical utility and flexibility of the alpha power transformed beta distribution, it is fitted to two real-life datasets and compared to commonly known probability distributions such as the Weibull, exponential Weibull, Beta, and Kumaraswamy beta distributions. It offers a superior fit to the data considered. The distribution reviales of the microbes reveald a wide range of shapes of probability density functions and flexible hazard rates. The distribution is a new contribution to the field of statistical and probability theory. The findings of the study can be used as a basis for future research in the area of statistical science and health.

Keywords

• alpha power transformation
• APT beta
• beta probability distrubtion
• parameter estimation
• probability distribution
• simulation