Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Se...Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.展开更多
The bivariate distributions are useful in simultaneous modeling of two random variables.These distributions provide a way to model models.The bivariate families of distributions are not much widely explored and in thi...The bivariate distributions are useful in simultaneous modeling of two random variables.These distributions provide a way to model models.The bivariate families of distributions are not much widely explored and in this article a new family of bivariate distributions is proposed.The new family will extend the univariate transmuted family of distributions and will be helpful in modeling complex joint phenomenon.Statistical properties of the new family of distributions are explored which include marginal and conditional distributions,conditional moments,product and ratio moments,bivariate reliability and bivariate hazard rate functions.The maximum likelihood estimation(MLE)for parameters of the family is also carried out.The proposed bivariate family of distributions is studied for the Weibull baseline distributions giving rise to bivariate transmuted Weibull(BTW)distribution.The new bivariate transmuted Weibull distribution is explored in detail.Statistical properties of the new BTW distribution are studied which include the marginal and conditional distributions,product,ratio and conditional momenst.The hazard rate function of the BTW distribution is obtained.Parameter estimation of the BTW distribution is also done.Finally,real data application of the BTW distribution is given.It is observed that the proposed BTW distribution is a suitable fit for the data used.展开更多
Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the depend...Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.展开更多
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah under grant number(D-153-130-1441).The author,therefore,gratefully acknowledge the DSR technical and financial support.
文摘Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.
文摘The bivariate distributions are useful in simultaneous modeling of two random variables.These distributions provide a way to model models.The bivariate families of distributions are not much widely explored and in this article a new family of bivariate distributions is proposed.The new family will extend the univariate transmuted family of distributions and will be helpful in modeling complex joint phenomenon.Statistical properties of the new family of distributions are explored which include marginal and conditional distributions,conditional moments,product and ratio moments,bivariate reliability and bivariate hazard rate functions.The maximum likelihood estimation(MLE)for parameters of the family is also carried out.The proposed bivariate family of distributions is studied for the Weibull baseline distributions giving rise to bivariate transmuted Weibull(BTW)distribution.The new bivariate transmuted Weibull distribution is explored in detail.Statistical properties of the new BTW distribution are studied which include the marginal and conditional distributions,product,ratio and conditional momenst.The hazard rate function of the BTW distribution is obtained.Parameter estimation of the BTW distribution is also done.Finally,real data application of the BTW distribution is given.It is observed that the proposed BTW distribution is a suitable fit for the data used.
基金supported by National Natural Science Foundation of China(11201345)China Postdoctoral Science Foundation(2015M572598)Natural Science Foundation of Zhejiang Province(LY15G010006)
基金supported by the National Natural Science Foundation of China(71571144 71401134)the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province(2016KW-033)
文摘Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.
