A Test of Separate Families of Distributions Based on the Empirical Moment Generating Function
针对总体分布属于某个指定分布族、备择假设属于另一分离分布族的检验问题，提出基于样本矩生成函数与理论矩生成函数差异的检验方法，并研究其大样本和小样本性质。
In testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply. We propose a test based on the difference between the sample moment generating function and its theoretical counterpart under Ho. The argument of the moment generating function is chosen to maximize the test's large-sample power. Small-sample properties of the test in two applications are studied by simulation.