Test Results For A Continuous Amount Of Adaptive Jar Model

In this paper we study the urn models with continuous trial outcome. The generalized Friedman's urn(GFU) model has been extensively applied to biostatistics. However, in the former literature, some results are established under the assumption that the outcome of the trial is dichotomous: a success or a failure. In fact, many trials may have a variety of outcomes, including success and failure. So the assumption that the outcome is continuous is reasonable too. Based on this assumption, we establish some adaptive models. We obtain some strong convergence theorems, rates of convergence, asymptotic normality of estimates. And then we design a new method to add balls by comparing the present trial's outcome with the average outcomes before. At last, we carry out a simulation to show that the 'comparing method' given in this paper makes better performance than the traditional way.