Example of Poisson Distribution-Wars by Year

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Presentation transcript:

Example of Poisson Distribution-Wars by Year Number of wars beginning by year for years 1482-1939. Table of Frequency counts and proportions (458 years): Total Wars: 0(242) + 1(148) + 2(49) + 3(15) + 4(4) = 307 Average Wars per year: 307 wars / 458 years = 0.67 wars/year

Using Poisson Distribution as Approximation Since mean of empirical (observed) distribution is 0.67, use that as mean for Poisson distribution (that is, set l = 0.67) p(0) = (e-ll0)/0! = e-0.67 = 0.5117 p(1) = (e-ll1)/1! = e-0.67(0.67) = 0.3428 p(2) = (e-ll2)/2! = e-0.67(0.67)2/2 = 0.1149 p(3) = (e-ll3)/3! = e-0.67(0.67)3/6 = 0.0257 p(4) = (e-ll4)/4! = e-0.67(0.67)4/24 = 0.0043 P(Y5) = 1-P(Y4)= 1-.5117-.3428-.1149-.0257-.0043=0.0006

Comparison of Observed and Model Probabilities In EXCEL, the function =POISSON.DIST(y,l,FALSE) returns p(y) = e-lly/y! The model provides a good fit to the observed data. Formal tests of goodness-of-fit are covered in the sequel course.