Some generalized Burr XII distributions with applications to income and lifetime data

Abstract

The proposal of new continuous distributions by adding one or more shape parameter(s) to baseline models has attract researchers of many areas. Several generators have been studied in recent years that can be described as special cases of the transformed-transformer (T-X) method. The gamma generalized families (“gamma-G” for short), called Zografos-Balakrishnan-G (Zografos and Balakrishnan, 2009) and Ristic-Balakrishnan-G (Ristic and Balakrishnan, 2012), are important univariate distributions sub-families of the T-X generator. They are generated by gamma random variables. It was found that eighteen distributions have been studied as baselines in the gamma generalized families. Another known family of univariate distributions is generated by extending the Weibull model applied to the odds ratio G(x)=[1 – G(x)], called the Weibull-G (Bourguignon et al., 2014). It was found that seven distributions have been studied in the context of the Weibull-G family. The logistic-X (Tahir et al., 2016a) is also a sub-family on the T-X generator that was recently introduced in the literature. Considering this approach, we discuss in this thesis the gamma-G, logistic-X and Weibull-G families by taking the Burr XII distribution as baseline. We present density expansions, quantile functions, ordinary and incomplete moments, generating functions, estimation of the model parameters by maximum likelihood and provide applications to income and lifetime real data sets for the proposed distributions. We show that the new distributions yield good adjustments for the considered data sets and that they can be used effectively to obtain better fits than other classical models and Burr XII generated families.