A FREQUENCY DISTRIBUTION REPRESENTED AS THE SUM OF 2 POISSON DISTRIBUTIONS
成果类型：
Article
署名作者：
SCHILLING, W
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.2307/2280544
发表日期：
1947
页码：
407-424
关键词：
摘要：
When an empirical distr. of objects or events appears theoretically likely to conform to a Poisson distr. but exhibits frequencies significantly different from the theoretical, one very simple alternative hypothesis is that the distr. consists of the sum of 2 Poissons. It is considered that n1 events out of a total frequency n were distributed in the Poisson manner with mean a1 and that the remaining n 2 events were distributed according to another Poisson with mean [alpha] 2. The general term for frequency class x of the combined distr. then becomes: [image] Simple equations are derived for fitting this distr. using moments, and the Chi-square test for goodness of fit is discussed. Several empirical distrs. having o 2>x>1 and departing from a single Poisson are adequately fitted by the summed distr. and possible interpretations are offered. For example, an infrequent category of death might have one mean value during summer and another during winter resulting in a long-period distr. of the described type.