el-Shaarawi A H
Appl Environ Microbiol. 1985 May;49(5):1304-6. doi: 10.1128/aem.49.5.1304-1306.1985.
Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.
本文介绍了关于泊松加附加零分布和截断泊松分布的推断方法，并通过细菌学数据进行了说明。其中一些方法旨在检验零频率与泊松分布的兼容性，而其他方法则用于检验截断泊松分布的拟合优度。特别地，提出了一种适用于截断情况的修正形式的费希尔离散指数。结果表明，使用通常的离散指数表达式来检验截断泊松分布的适用性是不正确的，并且会导致比基于显著性检验预期更频繁地接受不合适的拟合。此外，还提出了三个检验统计量来检验零频率与泊松分布得兼容性。模拟结果表明，两个检验统计量，一个由 Cochr an（W.G.Cochran，《生物统计学》10:417 - 451，1954）提出，另一个由Rao和Chakravarti（C.R.Rao和I.M.Chakravarti，《生物统计学》12:264 - 282，1956）提出，比似然比检验的统计量更可取。
