Abstract: The scheme of doubly type-II censored sampling is an important method of obtaining data in lifetime studies. Statistical analysis of life time distributions under this censoring scheme is based on precise lifetime data. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. This paper deals with the prob lem of estimating the scale parameter of Rayleigh distribution under doubly type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. We propose a new method to determine the maximum likelihood estimate of the parameter of interest. The asymptotic variance of the ML estimate is then derived by using the missing information principle. Their performance is then assessed through Monte Carlo simulations. Finally, an illustrative example with real data concerning 25 ball bearings in a life test is presented.
Abstract: Copulas have recently emerged as practical methods for multivari ate modeling. To our knowledge, only a limited amount of work has been done to apply copula-based modeling in context analysis. In this study, we generalized Clayton copula under the appropriate weighted function. In some examples, bivariate distributions by using the weighted Clayton cop ula are generalized. Also the properties of generalized Clayton copula are provided. The Clayton copula and weighted Clayton model cannot be used for negative dependence. These have been used to study left tail depen dence. This property is stronger in weighted Clayton model with respect to ordinary Clayton copula. It will also be shown that the generalized Clayton copula is suitable for the probable modeling of the hydrology data.