On the Generalized Log Burr III Distribution: Development, Properties, Characterizations and Applications

Abstract

In this paper, we present a generalized log Burr III (GLBIII) distribution developed on the basis of a generalized log Pearson differential equation (GLPE). The density function of the GLBIII is exponential, arc, J, reverse-J, bimodal, left-skewed, right- skewed and symmetrical shaped. The hazard rate function of GLBIII distribution has various shapes such as constant, increasing, decreasing, increasing-decreasing, upside- down bathtub and modified bathtub. Descriptive measures such as quantile function, sub- models, ordinary moments, moments of order statistics, incomplete moments, reliability and uncertainty measures are theoretically established. The GLBIII distribution is characterized via different techniques. Parameters of the GLBIII distribution are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). Goodness of fit of this distribution through different methods is studied. The potentiality and usefulness of the GLBIII distribution is demonstrated via its applications to two real data sets

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