Generalized Log Burr XII Distribution

Abstract

Burr distributions are frequently used for modeling business failure data, modeling finance, insurance data, failure time modeling, reliability and acceptance sampling plan. In this research work, we present a new distribution “Generalized Log Burr XII (GLBXII) Distribution” developed on the basis of the generalized log Pearson differential equation. The purposed distribution generalizes many new distributions and some existing distributions. The main objective of this research is to develop theoretical properties as well as some numerical study of GLBXII distribution. Some structural and mathematical properties including moments, inequality measures, uncertainty measures and reliability measures are theoretically derived. Characterizations of GLBXII distribution are presented through conditional expectation, doubly truncated moments and ratio of truncated moments. The generalized log Weibull distribution is ascertained as limiting distribution of GLBXII distribution. GLBXII distribution is obtained from compounding mixture of distributions. The potentiality of GLBXII distribution is checked by its application to real data sets. Parameters of purposed distribution, sub-models and competing models are estimated using maximum likelihood method. Goodness of fit of purposed distribution through different methods is studied. The purposed distribution is best fit than the sub-models and competing models distribution. Finally we come to know that Generalized log Burr XII (GLBXII) distribution is best fit than log Burr XII (LBXII), log Lomax (LL), generalized Burr XII (GBXII), and Burr XII(BXII) distribution.