Step 1 : Find expected value (deaths per corp per year)
k = 91+32+11+2+144
eV = 0*(144/k) + 1*(91/k) + 2*(32/k) + 3*(11/k) + 4*(2/k)
eV
## [1] 0.7
Step 2 : Apply poisson dist.
#Side note : Does R have a numerical e value?
poissonFit = function(x){
e = (1+1/99999)^99999
return( 280 *( ( (.7^x)*e^-.7 /factorial(x) ) ))
}
deaths = c(0,1,2,3,4)
von_Bortkiewicz = c(144,91,32,11,2)
poissoned_eVs = sapply(deaths,poissonFit)
cbind(deaths,von_Bortkiewicz,poissoned_eVs)
## deaths von_Bortkiewicz poissoned_eVs
## [1,] 0 144 139.044372
## [2,] 1 91 97.331060
## [3,] 2 32 34.065871
## [4,] 3 11 7.948703
## [5,] 4 2 1.391023
I’d say the distribution is appropriate, as the number of deaths increase so does the difference of the poisson distribution and von_B’s records.