TRANSMUTED TYPE I GENERAL EXPONENTIAL FAMILY OF DISTRIBUTIONS

Abstract

The Transmuted Type I General Exponential family of distributions as a new generator is proposed and studied. The new generator has a closed form and therefore very tractable, its hazard rate function has the flexibility to model different kinds of the bathtub shapes. Also, a comprehensive description of the statistical properties of the new generator including explicit expressions for the ordinary and incomplete moments, moments generating function, order statistics and stochastic ordering property are derived. Five special models were derived from the proposed generator. The unknown parameters of the models were estimated and the Monte Carlo Simulation technique was used to assess the performance of the maximum likelihood estimators in terms of the average biases and the root mean squared errors, and it was found that the estimators are stable. The dynamism of the proposed generator was demonstrated by using real datasets and it was shown that the special models of the proposed generator provide a better fit than other competing models. It is recommended that the new family of distributions can be used in broad application in real life situation.