A Generator of Bivariate Distributions: Properties, Estimation, and Applications (original) (raw)
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A new bivariate distribution is proposed in this paper using the univariate modified Weibull extension distribution. The proposed distribution is referred to as the bivariate Modified Weibull Extension (BMWE) distribution. The BMWE distribution is of Marshall-Olkin type. We discuss some of the statistical properties of the BMWE distribution. Applications of this distribution to dependent competing risks data are discussed. The maximum likelihood estimators (MLE) of the model parameters using both bivariate data and dependent competing risks data are discussed. These MLE's cannot be obtained in closed form. Therefore, numerical optimization methods are applied. A simulation study is carried out to investigate the performance of the estimation technique. Two real data sets; one bivariate data set and another dependent competing risks data set, are analyzed using the proposed distribution for illustrative and comparison purposes.
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Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the co...
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A new class of bivariate distributions is presented in this paper. The procedure used in this paper is based on a latent random variable with exponential distribution. The model introduced here is of Marshall-Olkin type. A mixture of the proposed bivariate distributions is also discussed. The results obtained here generalize those of the bivariate exponential distribution present in the literature.
A new family based on lifetime distribution: Bivariate Weibull-G models based on Gaussian copula
International Journal of ADVANCED AND APPLIED SCIENCES
Copula method plays an essential rule to study the dependence between data variables especially in bivariate distribution. It is noted that some bivariate models are constructed with uncomplete information of distributions. Copula improves the reliability of applications such as flood peak. Weibull distribution is a popular used in engineering, theory, medical and survival analysis. Despite its spread, it is known that the Weibull distribution could not implement the data set with non-monotone failure rate. In such case, many papers have suggested a modification and generalization of Weibull model. One of generalization is made through the baseline distribution by adding more shape parameters. The main purpose of our paper is to present some new bivariate Weibull models with respect to G cumulative distributions of baseline distribution. This approach converges the power series of probability distribution. We use the copula function to construct the bivariate Weibull distribution. The proposed models provide high flexibility and can be used effectively for modeling dataset with a different structure. We provide special cases in details namely; bivariate Weibullexponential, bivariate Weibull-Rayleigh and bivariate Weibull Chi-square. We use Gaussian copula function to merge the dependent distributions, this copula is popular used in various applications like econometrics and finance. We discuss some structural properties of the proposed models. In order to estimate the model parameters, we discuss parametric methods via maximum likelihood estimation and modified maximum likelihood methods. In addition, we use the moment methods as semi-parametric methods for parameters estimations. Finally, Simulations are studied to illustrate methods of inference discussed and study the performance of new distributions.
An order-statistics-based method for constructing multivariate distributions with fixed marginals
Journal of Multivariate Analysis, 2008
A new system of multivariate distributions with fixed marginal distributions is introduced via the consideration of random variates that are randomly chosen pairs of order statistics of the marginal distributions. The distributions allow arbitrary positive or negative Pearson correlations between pairs of random variates and generalise the Farlie-Gumbel-Morgenstern distribution. It is shown that the copulas of these distributions are special cases of the Bernstein copula. Generation of random numbers from the distributions is described, and formulas for the Kendall and grade (Spearman) correlations are given. Procedures for data fitting are described and illustrated with examples.
Mathematics
For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-We...