Abstract
In this paper, we define and study a four-parameter model called the transmuted Burr XII distribution. We obtain some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics, probability weighted moments and entropies. We formulate and develop a log-linear model using the new distribution so-called the log-transmuted Burr XII distribution for modeling data with a unimodal failure rate function, as an alternative to the log-McDonald Burr XII, log-beta Burr XII, log-Kumaraswamy Burr XII, log-Burr XII and logistic regression models. The flexibility of the proposed models is illustrated by means of three applications to real data sets.
Highlights
There has been an increased interest among statisticians in proposing new methods to generate univariate continuous distributions, which have been extensively used for modeling data in several applied sciences such as engineering, lifetime analysis, economics, medical and actuarial studies, demography, finance and insurance
We provide an application for the log-transmuted Burr XII (LTBXII) regression model
These results indicate that the LTBXII regression model has the lowest AIC, BIC and CAIC values among those values of the fitted models, and it could be chosen as the best model
Summary
There has been an increased interest among statisticians in proposing new methods to generate univariate continuous distributions, which have been extensively used for modeling data in several applied sciences such as engineering, lifetime analysis, economics, medical and actuarial studies, demography, finance and insurance. Consider a baseline cumulative distribution function (cdf) tt(x; φ) and probability density function (pdf) g(x; φ) depending on a parameter vector φ = The cdf and pdf of the transmuted-G (TG) family of distributions are defined by. They do not investigated its regression, applications and several properties of the TBXII distribution. The main objective of this paper is to study the TBXII distribution defined from the TG family and give a comprehensive account of some of its mathematical properties.
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