We introduce the four-parameter Kumaraswamy Gompertz distribution. We obtain the moments, generating and quantilefunctions, Shannon and Rényi entropies, mean deviations and Bonferroni and Lorenz curves. We provide a mixture representation for the density function of the order statistics. We discuss the estimation of the model parameters by maximum likelihood. We provide an application a real data set that illustrates the usefulness of the new model.
Abstract: We introduce a new class of the slash distribution using folded normal distribution. The proposed model defined on non-negative measure ments extends the slashed half normal distribution and has higher kurtosis than the ordinary half normal distribution. We study the characterization and properties involving moments and some measures based on moments of this distribution. Finally, we illustrate the proposed model with a simulation study and a real application.
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.
Abstract: We study a new five-parameter model called the extended Dagum distribution. The proposed model contains as special cases the log-logistic and Burr III distributions, among others. We derive the moments, generating and quantile functions, mean deviations and Bonferroni, Lorenz and Zenga curves. We obtain the density function of the order statistics. The parameters are estimated by the method of maximum likelihood. The observed information matrix is determined. An application to real data illustrates the importance of the new model.
We introduce a new family of distributions namely inverse truncated discrete Linnik G family of distributions. This family is a generalization of inverse Marshall-Olkin family of distributions, inverse family of distributions generated through truncated negative binomial distribution and inverse family of distributions generated through truncated discrete Mittag-Leffler distribution. A particular member of the family, inverse truncated negative binomial Weibull distribution is studied in detail. The shape properties of the probability density function and hazard rate, model identifiability, moments, median, mean deviation, entropy, distribution of order statistics, stochastic ordering property, mean residual life function and stress-strength properties of the new generalized inverse Weibull distribution are studied. The unknown parameters of the distribution are estimated using maximum likelihood method, product spacing method and least square method. The existence and uniqueness of the maximum likelihood estimates are proved. Simulation is carried out to illustrate the performance of maximum likelihood estimates of model parameters. An AR(1) minification model with this distribution as marginal is developed. The inverse truncated negative binomial Weibull distribution is fitted to a real data set and it is shown that the distribution is more appropriate for modeling in comparison with some other competitive models.