Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied.