A New Generalized Weibull- Odd Frѐchet Family of Distributions: Statistical Properties and Applications
A. Usman *
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.
S. I. S. Doguwa
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.
B. B. Alhaji
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria. and Nigerian Defence Academy, Kaduna, Nigeria.
A. T. Imam
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
We introduced a new generalized Weibull- Odd Frѐchet family of distributions with three extra parameters and we derived some of its structural properties. We derived comprehensive mathematical properties which include moments, moment generating function, Entropies and Order Statistics. One family of this distribution called new generalized Weibull- Odd Frѐchet -Frѐchet distribution is used to fit two data sets using the MLE procedure. A Monte Carlo simulation is used to test the robustness of the parameters of this distribution, in terms of the bias and mean squared error. The results of fitting this new distribution to two different data sets suggest that the new distribution outperforms its competitors.
Keywords: New generalized Weibull- odd Frѐchet family, order statistic, entropies, Monte Carlo simulation.