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Zografos–Balakrishnan Burr XII Distribution: Regression Modeling and Applications

Afaq Altun, Haitham M. Yousof, Subrata Chakraborty, Laba Handique


In this paper, we propose a new three-parameter model called the Zografos–Balakrishnan Burr XII distribution, which extends the Burr XII model. The new density function is expressed as a linear mixture of Burr XII densities. Explicit expressions for some of its mathematical and statistical characteristics including the ordinary and incomplete moments, quantile, cumulants, generating functions and order statistics are derived. We propose
a log-linear regression model using a new distribution, the log Zografos–Balakrishnan BXII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation is discussed. The proposed model is shown to provide better fits than some nested and non nested models by using five real data sets. We hope that the proposed model will attract
wider applications in areas such as survival and lifetime data, meteorology, hydrology, engineering and others.


Burr XII distribution, Zografos–Balakrishnan Family, Regression Modeling, Maximum Likelihood, Moments, Order Statistics.

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