The four-parameter Burr XII distribution: Properties,regression model,and applications |
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Authors: | Ahmed Z Afify Gauss M Cordeiro Edwin M M Ortega Haitham M Yousof Nadeem Shafique Butt |
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Institution: | 1. Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egyptahmed.afify@fcom.bu.edu.eg;3. Departamento de Estatística, Universidade Federal de Pernambuco, Recife, Brazil;4. Departamento de Ciências Exatas, Universidade de S?o Paulo, Piracicaba, SP, Brazil;5. Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt;6. Department of Family and Community Medicine, KAU, Jeddah, Saudi Arabia |
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Abstract: | This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data. |
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Keywords: | Burr XII maximum likelihood moments order statistics Weibull G-family |
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