伽玛混合分布中的齐一性检验
TEST FOR HOMOGENEITY UNDER GAMMA MIXTURE MODEL
伽玛分布族被广泛应用于可靠性理论研究,生存数 据和财务数据分析. 文章研究使用EM方法来检验伽马混合模型的齐一性. 我们专注于双参数伽玛分布,这是一个具有自由度和尺度参数的分布族. 文章把伽玛混合模型中的尺度参数限制为一个结构参数. 由于有限混合模型不满足正则性条件,经典似然比检验的极限分布不 是通常的卡方. 近年来发展的修正似然比检验及EM方法皆可用来检验伽马混合模型的齐一性. 然而,当应用于伽马混合模型时,这些检验的适用性必须重新验证. 文章得到了EM检验的极限分布并利用模拟计算提供了其犯一类错误的概率的信息, 以及它在多个设置下的功效.还提供了一个数据的例子来说明如何使用这种方法.
Gamma distribution family is broadly used in liability theory, life time data analysis and financial statistics. We study the use of EM-test for homogeneity under a gamma mixture model. We focus on two-parameter gamma distribution, one is the degree of freedom and the other is the scale parameter. In this paper, the scale parameter is confined to be a structure parameter in the gamma mixture. Due to non--regularity of finite mixture models, the classical likelihood ratio test does not have a usual chisquared limiting distribution. The recently developed modified likelihood ratio test and EM-test are believed to be effective approaches. However, when applied to gamma mixture models, their properties must be validated individually. In this paper, we derive the limiting distribution of the EM-test. The simulations are used to provide its empirical type-I errors and powers under various settings. A real data example is used to illustrate the use of this method.
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