On the Topp Leone Exponentiated-G Family of Distributions: Properties and Applications
Sule Ibrahim *
Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
Sani Ibrahim Doguwa
Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
Isah Audu
Department of Statistics, Faculty of Physical Sciences, Federal University of Technology, Minna, Nigeria.
Jibril Haruna Muhammad
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.
Keywords: Hazard rate, reliability, Kumarasway, Lehmann alternative, order statistics