Journal of Data Science

The odd inverse Pareto-Weibull distribution is introduced as a new lifetime distribution based on the inverse Pareto and the T-X family. Some mathematical properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. The importance and flexibility of the proposed model are assessed using a real data.

In this article, we introduce an extension referred to as the exponentiated Weibull power function distribution based on the exponentiated Weibull-G family of distributions. The proposed model serves as an extension of the two-parameter power function distribution as well as a generalization to the Weibull power function presented by Tahir et al. (2016 a). Various mathematical properties of the subject distribution are studied. General explicit expressions for the quantile function, expansion of density and distribution functions, moments, generating function, incomplete moments, conditional moments, residual life function, mean deviation, inequality measures, Rényi and q – entropies, probability weighted moments and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. Finally, the practical importance of the proposed distribution is examined through three real data sets. It has been concluded that the new distribution works better than other competing models.

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.

The Pareto distribution is a power law probability distribution that is used to describe social scientific, geophysical, actuarial, and many other types of observable phenomena. A new weighted Pareto distribution is proposed using a logarithmic weight function. Several statistical properties of the weighted Pareto distribution are studied and derived including cumulative distribution function, location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life, moments, shape indices such as skewness and kurtosis coefficients and order statistics. A parametric estimation is performed to obtain estimators for the distribution parameters using three different estimation methods the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution. The distribution is fitted to a real data set to show its importance in real life applications.

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.