Communication in Physical Sciences 2020, 7(3):147-163 Available at https://journalcps.com/index.php/volumes Communication in Physical Sciences, 2020, 7(3): 147-163 A Type I Half Logistic Exponentiated-G Family of Distributions: Properties and Application Olalekan Akanji Bello * , Sani Ibrahim Doguwa, Abubakar Yahaya and Haruna Mohammed Jibril Received: 12 June 2021/Accepted 09 September 2021/Published online: 14 September 2021 Abstract: Several new improved, generalized, and extended families of distributions have been discovered in recent years from families of distributions to aid their application in a variety of fields. The Type I half-logistic exponentiated- G family of distributions which generalizes and extends the Type I half-logistic family of distributions, with two extra positive shape parameters is investigated and proposed. We discuss some of the statistical properties of the proposed family such as explicit expressions for the quantile function, ordinary and incomplete moments, generating function, reliability and order statistics. Some of the new family’s sub- models are discussed. We discuss the estimation of the model parameters by method of maximum likelihood. Two real data sets are employed to show the applicability and flexibility of the new family. Keywords: Hazard rate, Reliability, Exponentiated-G, Type I Half Logistic G, Maximum likelihood, Order Statistics. Olalekan Akanji Bello * Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria Email: olalekan4sure@gmail.com Orcid id: 0000-0002-2209-9035 Sani Ibrahim Doguwa Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria. Email: sidoguwa@gmail.com Orcid id: 0000-0002-5779-2358 Abubakar Yahaya Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria. Email: ensiliyu2@yahoo.co.uk Orcid id: 0000-0002-1453-7955 Haruna Mohammed Jibril Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria Email: alharun2004@yahoo.com Orcid id: 0000-0001-7869-1807 1.0 Introduction Statistical distributions are frequently used to describe real-life events and the theory of statistical distributions can be is intensively studied to obtain novel distributions for optimum utility. In statistics, there is a significant desire to construct more flexible statistical distributions. Many different types of generalized distributions have been devised and applied to various phenomena. Several continuous univariate distributions have been extensively used for modeling data in many areas such as economics, engineering, biological studies and environmental sciences (Johnson et al., 1994). However, applications in areas such as finance, lifetime analysis and insurance clearly require extended forms of these distributions. Consequently, several classes of distributions have been constructed by extending common families of continuous distributions. Generated family of continuous distributions is a new improvement for creating and extending the usual classical distributions. The newly generated families have been broadly studied in several areas and have been observed to