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This paper proposes a new generalization of the Gull Alpha Power Family of distribution, namely the exponentiated generalized gull alpha power family of distribution abbreviated as (EGGAPF) with two additional parameters. This proposed family of distributions has some well known sub-models. Some of the basic properties of the distribution like the hazard function, survival function, order statistics, quantile function, moment generating function are investigated. In order to estimate the parameters of the model the method of maximum likelihood estimation is used. To assess the performance of the MLE estimates a simulation study was performed. It is observed that with increase in sample size, the average bias, and the RMSE decrease. A distribution from this family is fitted to two real data sets and compared to its sub-models. It can be concluded that the proposed distribution outperforms its sub-models.
Kilai et al. (2022) studied this question.