论文标题
离散分布的有条件拟合测试
Conditional Goodness-of-Fit Tests for Discrete Distributions
论文作者
论文摘要
在本文中，我们解决了测试拟合优度以进行离散分布的问题，我们将重点放在几何分布上。我们使用β几何分布和I类离散的Weibull分布作为替代分布来定义新的基于可能的拟合测试。在一项模拟研究中比较了测试，其中还考虑了经典的拟合测试以进行比较。在整个论文中，我们考虑了在零假设下具有最小足够统计量的有条件测试，这可以计算精确的p值。为此，开发了一种新方法，用于从几何分布和负二项式分布中绘制条件样本。我们还简要解释了如何为二项式，负二项式和泊松分布修改条件方法。最终注意到，通过使用Metropolis-Hastings算法，模拟方法可以扩展到具有相同统计量的其他离散分布。
In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where we focus on the geometric distribution. We define new likelihood-based goodness-of-fit tests using the beta-geometric distribution and the type I discrete Weibull distribution as alternative distributions. The tests are compared in a simulation study, where also the classical goodness-of-fit tests are considered for comparison. Throughout the paper we consider conditional testing given a minimal sufficient statistic under the null hypothesis, which enables the calculation of exact p-values. For this purpose, a new method is developed for drawing conditional samples from the geometric distribution and the negative binomial distribution. We also explain briefly how the conditional approach can be modified for the binomial, negative binomial and Poisson distributions. It is finally noted that the simulation method may be extended to other discrete distributions having the same sufficient statistic, by using the Metropolis-Hastings algorithm.
