Applications of Poisson's Probability Summation

The applicability of Poisson's exponential summation to a variety of actual data is illustrated by thirty-two examples of actual frequency-distributions to which the Poisson distribution is a fairly good approximation. The comparison of actual and theoretical distributions is made graphically, using as a background new probability curves showing Poisson's exponential summation with a logarithmic scale for the average. To suggest possible explanations of the observed deviations from the theoretical Poisson distribution consideration is given to the effect on the theoretical distribution of certain modifications in the underlying assumptions, corresponding to conditions under which much actual data must be obtained.