Applications of Poisson's Probability Summation

T h e a p p l i c a b i l i t y of Poisson's exponential s u m m a t i o n to a v a r i e t y of a c t u a l d a t a is illustrated by t h i r t y - t w o e x a m p l e s of a c t u a l freq u e n c y - d i s t r i b u t i o n s to which t h e Poisson d i s t r i b u t i o n is a fairly good a p p r o x i m a t i o n . T h e c o m p a r i s o n of a c t u a l a n d theoretical d i s t r i b u t i o n s is m a d e graphically, using as a b a c k g r o u n d new p r o b a b i l i t y c u r v e s showing Poisson's e x p o n e n t i a l s u m m a t i o n with a l o g a r i t h m i c scale for t h e a v e r a g e . To suggest possible e x p l a n a t i o n s of t h e observed d e v i a t i o n s f r o m t h e theoretical Poisson d i s t r i b u t i o n c o n s i d e r a t i o n is given to t h e effect on t h e t h e o r e t i c a l d i s t r i b u t i o n of c e r t a i n modifications in t h e u n d e r l y i n g a s s u m p tions, c o r r e s p o n d i n g t o conditions u n d e r which m u c h a c t u a l d a t a m u s t b e obtained.