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//Caption: Kolmogorov-Smirnov Test
//Example9.9
//Page323
//Ho: The given set of observations follows normal distribution
//H1: The given set of observations does not follow the normal distribution
clear;
clc;
X =[0,5;5,10;10,15;15,20;20,25;25,30;30,35]; //Demand
o = [4,9,15,20,18,7,5]; //Observed frequency
alpha = 0.10; //significance level
n = sum(o); //total observed frequency
[m1,n1] = size(X);
for i = 1:m1
Xmid(i) = sum(X(i,:))/2;
Xo(i)= Xmid(i)*o(i);
end
Xioi = sum(Xo);
u = Xioi/n; //mean demand
N = length(Xmid);//Number of ranges for the random variable
Var = variance(Xmid)/2;
Std = sqrt(Var);
alpha = 0.10;//significance level
for i =1:N
Z_Stand(i) = (Xmid(i)-u)/Std;
[P(i),Q(i)]=cdfnor("PQ",Xmid(i),u,Std)
end
op = o/n;
EF = cumsum(op);
disp(op,'Observered probability=')
disp(Z_Stand,'Calculated z value=');
disp(P,'Observed cumulative Probability Z(OF) =');
disp(EF,'Expected cumulative probability EF = ');
for i = 1:N
D(i) = abs(P(i)-EF(i));
end
[Dcal,ind] = max(D);
Dn = 1.22/sqrt(n);
disp(D,'Calculated D values Di = ');
disp(Dcal,'Maximum D value Dcal =');
disp(Dn,'Theoritical D value of Dn for the sample size n =78, D78 =');
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
//
// Observered probability=
//
// 0.0512821 0.1153846 0.1923077 0.2564103 0.2307692 0.0897436 0.0641026
//
// Calculated z value=
//
// - 1.980747
// - 1.3260933
// - 0.6714397
// - 0.0167860
// 0.6378677
// 1.2925213
// 1.947175
//
// Observed cumulative Probability Z(OF) =
//
// 0.0238098
// 0.0924044
// 0.2509702
// 0.4933037
// 0.7382201
// 0.9019117
// 0.9742431
//
// Expected cumulative probability EF =
//
// 0.0512821 0.1666667 0.3589744 0.6153846 0.8461538 0.9358974 1.
//
// Calculated D values Di =
//
// 0.0274722
// 0.0742623
// 0.1080041
// 0.1220809
// 0.1079338
// 0.0339858
// 0.0257569
//
// Maximum D value Dcal =
//
// 0.1220809
//
// Theoritical D value of Dn for the sample size n =78, D78 =
//
// 0.1381378
//
// Since Dcal is less than the table value Dn accept the null hypothesis Ho
//
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