Maximum Likelihood Estimation in an Alpha-Power

The rest of this paper is organized as follows. In Section 2 we introduce and illustrate the new family. In Section 3 we derive the quantile function of the APTA-F family of distributions. In Section 4, we discuss approximate random sampling from the APTAF family of distributions, and maximum likelihood stimation in Section 5. Section 6 presents simulation results associated with the APTA-F family of distributions, assuming F follows the Weibull distribution as defined in Section 2. Section 7 discusses usefulness of the APTA-F family of distributions in fitting real-life data. Section 8 is devoted to the conclusions.