Journal of Data Science

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.

In this paper, we proposed another extension of inverse Lindley distribution, called extended inverse Lindley and studied its fundamental properties such as moments, inverse moments, mean deviation, stochastic ordering and entropy. The flexibility of the proposed distribution is shown by studying monotonicity properties of density and hazard functions. It is shown that the distribution belongs to the family of upside-down bathtub shaped distributions. Maximum likelihood estimators along with asymptotic confidence intervals are constructed for estimating the unknown parameters. An algorithm is presented for random number generation form the distribution. The property of consistency of MLEs has been verified on the basis of simulated samples. The applicability of the extended inverse Lindley distribution is illustrated by means of real data analysis.

In this paper, a new version of the Poisson Lomax distributions is proposed and studied. The new density is expressed as a linear mixture of the Lomax densities. The failure rate function of the new model can be increasing-constant, increasing, U shape, decreasing and upside down-increasing. The statistical properties are derived and four applications are provided to illustrate the importance of the new density. The method of maximum likelihood is used to estimate the unknown parameters of the new density. Adequate fitting is provided by the new model.

Abstract: The generalized gamma model has been used in several applied areas such as engineering, economics and survival analysis. We provide an extension of this model called the transmuted generalized gamma distribution, which includes as special cases some lifetime distributions. The proposed density function can be represented as a mixture of generalized gamma densities. Some mathematical properties of the new model such as the moments, generating function, mean deviations and Bonferroni and Lorenz curves are provided. We estimate the model parameters using maximum likelihood. We prove that the proposed distribution can be a competitive model in lifetime applications by means of a real data set.

Abstract: Chen, Bunce and Jiang [In: Proceedings of the International Con ference on Computational Intelligence and Software Engineering, pp. 1-4] claim to have proposed a new extreme value distribution. But the formulas given for the distribution do not form a valid probability distribution. Here, we correct their formulas to form a valid probability distribution. For this valid distribution, we provide a comprehensive treatment of mathematical properties, estimate parameters by the method of maximum likelihood and provide the observed information matrix. The flexibility of the distribution is illustrated using a real data set.