Testing for censored bivariate distributions with applications to environmental data

Analysis of censored environmental data has been of special interest to many scientists and practitioners for the recent years. Numerous works have been published on modeling bivariate environmental data when variables of interest are below some detection limits. Depending on the problem, one of the variables or both variables may be unobserved. These situations especially arise in modeling the joint distributions of environmental variables such as flood, drought and epidemiological. Some of these variables cannot be observed as they are too small to be detected below certain threshold points. Because of this censored structure, it is difficult to assess the validity of proposed bivariate distributions. Moreover, there is a wide need for a simple goodness-of-fit test for researchers working on practical environmental problems. This motivates us to propose a goodness-of-fit test for location-scale type bivariate distributions with censored data. The asymptotic distribution of the proposed test is shown to have a Chi-square distribution. A simulation study is carried out to show the power performances of the test. A real environmental data from the literature is analyzed to illustrate the efficacy of our proposed test.