Abstract
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.
Highlights
In recent decades, many continuous univariate distributions have been developed but various data sets from reliability, insurance, finance, climatology, biomedical sciences and other areas do not follow these distributions
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
6.2 Characterization via Doubly Truncated Moment Here CRTMBIII-P distribution is characterized via doubly truncated moment
Summary
Many continuous univariate distributions have been developed but various data sets from reliability, insurance, finance, climatology, biomedical sciences and other areas do not follow these distributions. Modified, extended and generalized distributions and their applications to the problems in these areas is a clear need of day. The modified, extended and generalized distributions are obtained by the introduction of some transformation or addition of one or more parameters to the well-known baseline distributions. These new developed distributions provide better fit to the data than the sub and competing models. Shaw and Buckley (2009) proposed ranking quadratic transmutation map to solve financial problems
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