A New and Generalized Class of Log-logistic Modified Weibull Power Series Distributions with Applications

A new generalized class of distributions called the log -logistic modified Weibull power series (LLoGMWPS) distribution is developed and presented. The LLoGMWPS class of distributions generalizes several distributions including the log -logistic exponential power series, log -logistic Weibull power series, log -logistic Rayleigh power series, log -logistic power series class of distributions and a host of other distributions including log -logistic modified Weibull, log -logistic Weibull, and loglogistic distributions. The special case of the log -logistic modified Weibull Poisson (LLoGMWP) and log -logistic modified Weibull Logarithmic (LLoGMWL) distributions are studied in detail. We apply the method of maximum likelihood to estimate the parameters of this new distribution. Finally, real data examples are presented to illustrate the usefulness and applicability of both LLoGMWP and LLoGMWL distributions.