The Weibull Topp-Leone Generated Family of Distributions: Statistical Properties and Applications

Karamikabir, Hamid; Afshari, Mahmoud; Yousof, Haitham M.; Alizadeh, Morad; Hamedani, Gholamhossien

doi:10.29252/jirss.19.1.121

The Weibull Topp-Leone Generated Family of Distributions: Statistical Properties and Applications

Authors

Hamid Karamikabir ¹

Mahmoud Afshari ¹

Haitham M. Yousof ²

Morad Alizadeh ¹

Gholamhossien Hamedani ³

¹ Department of Statistics, Persian Gulf University, Bushehr, Iran

² Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt

³ Department of Mathematics, Statistics and Computer Science , Marquette University, USA

10.29252/jirss.19.1.121

Abstract

Statistical distributions are very useful in describing and predicting real world phenomena. Consequently, the choice of the most suitable statistical distribution for modeling given data is very important. In this paper, we propose a new class of lifetime distributions called the Weibull Topp-Leone Generated (WTLG) family. The proposed family is constructed via compounding the Weibull and the Topp-Leone distributions. It can provide better fits and is very flexible in comparison with the various known lifetime distributions. Several general statistical properties of the WTLG family are studied in details including density and hazard shapes, limit behavior, mixture representation, skewness and kurtosis, moments, moment generating function, incomplete moment. Different methods have been used to estimate its parameters. The performances of the estimators are numerically investigated. We have discussed inference on the new family based on the likelihood ratio statistics for testing some lifetime distributions. We assess the performance of the maximum likelihood estimators in terms of the biases and mean squared errors by means of a simulation study. The importance and flexibility of the new family are illustrated by means of two applications to real data sets.

Keywords

Generating Function

Lifetime Distributions

Maximum likelihood estimation

Quantile Function

Topp-Leone Distribution

Weibull distribution

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