Abstract
We propose a lifetime distribution with flexible hazard rate called cubic rank transmuted modified Burr III (CRTMBIII) distribution. We develop the proposed distribution on the basis of the cubic ranking transmutation map. The density function of CRTMBIII is symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped. The flexible hazard rate of the proposed model can accommodate almost all types of shapes such as unimodal, bimodal, arc, increasing, decreasing, decreasing-increasing-decreasing, inverted bathtub and modified bathtub. To show the importance of proposed model, we present mathematical properties such as moments, incomplete moments, inequality measures, residual life function and stress strength reliability measure. We characterize the CRTMBIII distribution via techniques. We address the maximum likelihood method for the model parameters. We evaluate the performance of the maximum likelihood estimates (MLEs) via simulation study. We establish empirically that the proposed model is suitable for strengths of glass fibers. We apply goodness of fit statistics and the graphical tools to examine the potentiality and utility of the CRTMBIII distribution.
Highlights
In recent decades, many continuous univariate distributions have been developed, various data sets from reliability, insurance, finance, climatology, biomedical sciences and other areas do not follow these distributions
We survey the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII distribution with respect to sample size n. This performance is done based on the following simulation study: Step 1: Generate 1000 samples of size n from the CRTMBIII distribution based on the inverse cdf method
We propose a very flexible distribution on the basis of the cubic transmuted mapping that is suitable for applications in survival analysis, reliability and actuarial science
Summary
Many continuous univariate distributions have been developed, various data sets from reliability, insurance, finance, climatology, biomedical sciences and other areas do not follow these distributions. 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. CUBIC RANK TRANSMUTED MODIFIED BURR III DISTRIBUTION: DEVELOPMENT, PROPERTIES, CHARACTERIZATIONS AND APPLICATIONS. The basic motivations for proposing the CRTMBIII distribution are: (i) to generate distributions with symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped; (ii) to obtain unimodal, bimodal, arc, increasing, decreasing, decreasing-increasingdecreasing, inverted bathtub and modified bathtub hazard rate function; (iii) to serve as the best alternative model for the current models to explore and modeling real data in economics, life testing, reliability, survival analysis manufacturing and other areas of research and (iv) to provide better fits than other sub-models.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
