Abstract
In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.
Highlights
Mahdavi and Kundu [1] introduced the alpha power transformation (APT) method to add an additional parameter to a family of distributions to increase flexibility in the given family
Weibull distribution by Ramadan and Magdy [6], the APT Lindley distribution by Dey et al [7], the APT inverseLindley distribution by Dey et al [8], the APT power Lindley studied by Hassan et al [9], and the APT Pareto distribution proposed in Ihtisham et al [10]
This section deals with some statistical properties of the alpha power transformed log-logistic (APTLL) distribution
Summary
Mahdavi and Kundu [1] introduced the alpha power transformation (APT) method to add an additional parameter to a family of distributions to increase flexibility (more applicable) in the given family. The cumulative distribution function (cdf) of an APT-G family is αGðxÞ − 1 Fðx ; αÞ = 64 α − 1 if α > 0, α ≠ 1, ð1Þ.
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