On the Generalized Transmuted-G Power Function Distribution

Abstract

In this research, the generalized transmuted-G family of distributions was used and applied to the power function distribution to obtain a new, more flexible probability distribution (the generalized transmuted-G power function distribution). This distribution is more flexible than the basic distributions under study. Some of its statistical properties were investigated, such as the probability density function, the cumulative density function, the survival and risk functions, and the reliability function. The parameters and reliability function of the generalized transmuted-G power function were estimated using the maximum likelihood method (Anderson-Darlingson (AD)). To determine the best method for estimating the parameters and reliability function, a brief simulation study was conducted using the Monte Carlo method. Several experiments were performed with small, medium, and large sample sizes (30, 50, 150, and 100) using two models with different values ​​for the unknown parameters. The mean squared error (MSE) was used as the statistical criterion for comparing the methods. In estimating parameters, the researcher concluded that the Anderson-Darlink (AD) method is superior for estimating unknown parameters and reliability functions for small and medium sample sizes.

On the practical side, the new probabilistic model (the generalized transmuted-G power function) was applied to real data (100 observations representing SPAP operating times). The performance of the proposed distribution was compared with the original power function distribution under study. The new model provided greater flexibility and efficiency in representing real data and proved superior in representing complex data.