Additive Weibull Log Logistic Distribution: Properties & Application

Saeed Hemeda


We introduce a new lifetime distribution with six parameters. This distribution is called the additive Weibull log logistic (AWLL) distribution based on the additive Weibull-generated family of distributions and the log logistic distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. Some statistical properties of the AWLL distribution including moments, incomplete moments, mean deviation, mode, median, skewness, and kurtosis are studied. Explicit expressions for the quantile function, moment-generating function and order statistics are obtained. The estimation of model parameters is discussed, using maximum likelihood method and the simulation study is conducted. The importance of the AWLL distribution is demonstrated through real data set compared with several lifetime distributions. 


Additive Weibull-G family, Log logistic, Moments, Order statistics, Reliability, Maximum likelihood estimation, Simulation

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