%stat351 stat351-goodness.m
%Goodness of fit test

%Testing Poisson distribution
>>accidents = [0 1 2 3 4 5]
 accidents =

     0     1     2     3     4     5
     
>> f = [10 30 40 20 5 5]
f =

    10    30    40    20     5     5


>> probability=months/110     
probability =
    0.0909    0.2727    0.3636    0.1818    0.0455    0.0455

>>lambda = sum(accidents.*probability)    
lambda =
    1.9545
        
>> poisspdf(0:5,lambda)    
ans =
    0.1416    0.2768    0.2705    0.1763    0.0861    0.0337

>>e=110*poisspdf(0:5,lambda)
e =
   15.5792   30.4502   29.7582   19.3879    9.4736    3.7033
>>Q=sum((f-e).^2./e)
 Q =
   8.1155
>>1-chi2cdf(Q,6-1)  
ans = 
    0.1500 %accept!

%Testing normality    
>>sigma = sqrt(sum((accidents - lambda).^2)/(6-1))
sigma =
    1.9639
p(1)=normcdf(0.5,lambda,sigma)
p(2)=normcdf(1.5,lambda,sigma)-normcdf(0.5,lambda,sigma)
p(3)=normcdf(2.5,lambda,sigma)-normcdf(1.5,lambda,sigma)
p(4)=normcdf(3.5,lambda,sigma)-normcdf(2.5,lambda,sigma)
p(5)=normcdf(4.5,lambda,sigma)-normcdf(3.5,lambda,sigma)
p(6)=1-normcdf(4.5,lambda,sigma)
p =
    0.2295    0.1790    0.2009    0.1749    0.1182    0.0975    
>>e=110*p    
e =
   25.2405   19.6927   22.1000   19.2437   13.0014   10.7217
>>Q=sum((f-e).^2./e)
Q =
   37.1030
>>1-chi2cdf(Q,6-1)
ans =
  5.7114e-007  %reject!