Burr X Exponential – G Family of Distributions: Properties and Application
A. A. Sanusi *
Department of Mathematics and Computer Science, Federal University of Kashere, Gombe State, Nigeria.
S. I. S. Doguwa
Department of Statistics, Ahmadu Bello University Zaria, Kaduna State, Nigeria.
I. Audu
Department of Statistics, Ahmadu Bello University Zaria, Kaduna State, Nigeria.
Y. M. Baraya
Department of Mathematics, Ahmadu Bello University Zaria, Kaduna State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we developed a new class of continuous distributions called Burr X Exponential-G Family. Also, we obtained sub-models of this family of distributions such as Burr X Exponential-Rayleigh (BXE-R) and Burr X Exponential Lomax (BXE-Lx) distributions; by showing their respective densities functions. Some structural properties of the proposed family of distributions were derived such as moment, moment generating function, probability weighted moment, renyi entropy and order statistics. We estimate the parameters of the model by using Maximum Likelihood methods. Finally, the results obtained are validated using two real data sets. The results show that BXE-Lx distribution provides better fit in the data sets than some other well known distributions. However, this new family of distributions will serve as an additional generator for developing new sub models to modeling positive real data sets.
Keywords: Burr X E – G family of distributions, Burr X exponential – Rayleigh distribution, Burr X exponential – Lomax distribution, moment generating function, Renyi entropy, order statistics, probability weighted moment, maximum likelihood estimation.