Zohdy M. Nofal

The generalized transmuted-G family of distributions

ABSTRACT We introduce a new class of continuous distributions called the generalized transmuted-G family which extends the transmuted-G class. We provide six special models of the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of three applications to real data sets.

The Weibull Fréchet distribution and its applications

ABSTRACT A new four-parameter lifetime model called the Weibull Fréchet distribution is defined and studied. Various of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and -entropies and order statistics are investigated. The new density function can be expressed as a linear mixture of Fréchet densities. The maximum likelihood method is used to estimate the model parameters. The new distribution is applied to two real data sets to prove empirically its flexibility. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in many areas.