The Alpha Power Muth-G Distributions and Its Applications in Survival and Reliability Analyses

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Abstract
The generalization of the family of distributions that could provide a simple, and efficient algorithm for parameter estimation and study of the behavior of datasets from various fields has received significant interest. Such a model has enormous advantages, such as its flexible nature, and the regression form can easily be derived. In the literature, various generalized families of distributions have been introduced. Despite the merits of these distributions, they still have some limitations due to many parameters in the model. Thus, the estimation of parameters often becomes cumbersome. Therefore, this study introduced the alpha power Muth or Teissier-G family of continuous distributions with well-defined parameters, and obtained the joint progressive type-II censoring scheme and their reliability measures. Furthermore, we obtained the global and local influences of the APTG model. We used real-life and simulated data to evaluate the numerical applications of the introduced model. The results show that the alpha power Muth or Teissier-G family of distributions gave the best fits to both datasets than some existing models.

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