We introduce the Generalized Rescaled P\'olya (GRP) urn. In particular, the GRP urn provides three different generative models for a chi-squared test of goodness of fit for the long-term probabilities of correlated data, generated by means of a reinforcement mechanism. Beside this statistical application, we point out that the GRP urn is a simple variant of the standard Eggenberger-P\'olya urn, that, with suitable choices of the parameters, shows "local" reinforcement, almost sure convergence of the empirical mean to a deterministic limit and different asymptotic behaviours of the predictive mean.
翻译:我们引入了通用的重标 P\'olya (GRP) URn 。 特别是, GRP URn 提供了三种不同的基因模型,用于通过强化机制对相关数据是否适合长期概率进行奇夸的测试。 除了这一统计应用外, 我们指出, GRP URn 是标准的 Eggenberger- P\'olya URn 的简单变体, 有了对参数的适当选择, 显示“ 本地” 强化, 几乎可以肯定经验意味着确定性限度和预测值的不同无症状行为。