محمود افشاری

In this paper, a new class of distributions called the odd log-logistic Burr-X family with two extra positive parameters is intro-duced and studied. The new generator extends the odd log-logistic and Burr X distributions among several other well-knowndistributions. We provide some mathematical properties of the new family including asymptotics, moments, moment-generatingfunction and incomplete moments. Different methods have been used to estimate its parameters such as maximum likelihood,least squares, weighted least squares, Cramer–von-Mises, Anderson–Darling and right-tailed Anderson–Darling methods. Weevaluate the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a sim-ulation study. Finally, the usefulness of the family is illustrated by means of three real data sets. The new models provide consis-tently better fits than other competitive models for these data sets. The new family is suitable for fitting different real data sets,the odd log-logistic Burr-X Normal model is used for modeling bimodal and skewed data sets and can be sued as an alternative tothe gamma-normal, beta-normal, McDonald-normal, Marshall-Olkin-normal, Kumaraswamy-normal, Zografos-Balakrishnanand Log-normal distributions.