Journal of Data Science

Abstract: The paper deals with the introduction of new generalized model i.e., Rayleigh Lomax distribution. In this manuscript, a comprehensive description of the various structural properties of the new proposed model including explicit expressions for moments, quantile function, generating functions and Renyi entropy have been given. The parameters of the newly developed distribution have been estimated using the technique of maximum likelihood estimation. Also, the generalized model has been compared with different models for illustration and best fit.

In this paper, we introduce a new four-parameter distribution called the transmuted Weibull power function (TWPF) distribution which e5xtends the transmuted family proposed by Shaw and Buckley [1]. The hazard rate function of the TWPF distribution can be constant, increasing, decreasing, unimodal, upside down bathtub shaped or bathtub shape. Some mathematical properties are derived including quantile functions, expansion of density function, moments, moment generating function, residual life function, reversed residual life function, mean deviation, inequality measures. The estimation of the model parameters is carried out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using real data sets.

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.

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.