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//Caption: Kolmogorov-Smirnov Test
//Example9.8
//Page322
//Ho: The given set of observations follows poisson distribution
//H1: The given set of observations does not follow the poisson distribution
clear;
clc;
X = [0,1,2,3,4,5,6]; //Arrival rate
o = [2,6,18,12,8,3,1];//Observed frequency
n = sum(o);//total observed frequencies
alpha = 0.05;//significance level
N = length(X); //Number of values of the random variable
for i = 1:length(X)
Xo(i)= X(i)*o(i);
end
Xioi = sum(Xo);
u = Xioi/n; //mean arrival rate
for i = 1:length(X)
P(i)= ((u^X(i))*exp(-u))/factorial(X(i));
end
op = o/n;
disp(op,'Observed Probability=');
disp(P,'Expected Probability=');
OF = cumsum(op);
EF = cumsum(P);
disp(OF,'Observed cumulative probability=')
disp(EF,'Expected cumulative probability=')
for i = 1:N
D(i) = abs(OF(i)-EF(i));
end
disp(D,'Calculated difference absolute value D =')
Dn = 1.36/sqrt(n);//theoretical value for a significance level of 0.05
disp(Dn,'Theoretical table value for a significance level of 0.05=')
[Dcal,ind]= max(D);
disp(Dcal,'The maximum value of D is Dcal=')
if (Dcal<Dn) then
disp('Since Dcal is less than the table value Dn accept the null hypothesis Ho')
else
disp('Sinc Dcal > Dn table value reject null hypothesis Ho')
end
//Result
// Observed Probability=
//
// 0.04 0.12 0.36 0.24 0.16 0.06 0.02
//
// Expected Probability=
//
// 0.0728029
// 0.1907435
// 0.2498740
// 0.2182233
// 0.1429362
// 0.0748986
// 0.0327057
//
// Observed cumulative probability=
//
// 0.04 0.16 0.52 0.76 0.92 0.98 1.
//
// Expected cumulative probability=
//
// 0.0728029
// 0.2635464
// 0.5134203
// 0.7316436
// 0.8745799
// 0.9494785
// 0.9821842
//
// Calculated difference absolute value D =
//
// 0.0328029
// 0.1035464
// 0.0065797
// 0.0283564
// 0.0454201
// 0.0305215
// 0.0178158
//
// Theoretical table value for a significance level of 0.05=
//
// 0.1923330
//
// The maximum value of D is Dcal=
//
// 0.1035464
//
// Since Dcal is less than the table value Dn accept the null hypothesis Ho
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