Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data
Maha A. Aldahlan
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.
Topics & Concepts
Logistic distributionQuantileLog-logistic distributionMathematicsStatisticsQuantile functionOrder statisticLogistic regressionMoment (physics)GeneralizationApplied mathematicsMoment-generating functionEntropy (arrow of time)Rényi entropyDistribution (mathematics)Principle of maximum entropyDistribution fittingProbability distributionMathematical analysisQuantum mechanicsPhysicsClassical mechanicsStatistical Distribution Estimation and ApplicationsProbabilistic and Robust Engineering DesignHydrology and Drought Analysis