ABSTRACT
Alpha particle radiation counts reported by Rutherford and Geiger in 1910 are used to illustrate a Poisson distribution. First described in 1837 by Poisson, the distribution was independently discovered by others, such as Newcomb in 1860 and Bateman in 1910. Some Stata functions for the Poisson distribution are shown. Variances, standard deviations, and standard errors are described for counts and rates. Using mortality data for Alzheimer’s disease, calculations are shown based on these formulae. Large sample Wald statistics and score statistics are described with formulae for rate differences and rate ratios. Confidence intervals are calculated. Exact methods are shown for P-values and confidence intervals. A Poisson process arises when counts are independent and their production is stationary. Several simulated examples are used to illustrate these principles. Overdispersion and underdispersion are described.
