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//Caption: Kolmogorov-Smirnov Test
//Example9.7
//Page321
//Ho: The given set of observations follows the uniform distribution
//H1: The given set of observations does not follow the uniform distribution
clear;
clc;
X = [30,31,32,33,34,35,36,37,38,39]; //Demand in tons
o = [2,3,1,4,2,2,4,2,4,1];//Observed frequency
n = sum(o);//total observed frequencies
alpha = 0.05;//significance level
N = length(X); //Number of values of the random variable
ExFre = n/N; //Expected frequency for each
disp(ExFre,'Expected Frequency for each =')
ExPr = ExFre/n;// Expected probability for each
disp(ExPr,'Expected probability for each=')
for i = 1:N
EP(i)= ExPr;
end
op = o./(N*ExFre);//Observed probability
disp(op,'Observed Probability=')
OF = cumsum(op);//Observed cumulative probability
disp(OF,'Observed Cumulative Probability OF =')
EF = cumsum(EP);//Expected cumulative probability
disp(EF,'Expected Cumulative Probability EF =')
for i = 1:N
D(i) = abs(OF(i)-EF(i));
end
disp(D,'Calculated difference absolute value D =')
Dn = 0.27;//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);
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
// Expected Frequency for each =
// 2.5
// Expected probability for each=
// 0.1
// Observed Probability=
// 0.08 0.12 0.04 0.16 0.08 0.08 0.16 0.08 0.16 0.04
// Observed Cumulative Probability OF =
// 0.08 0.2 0.24 0.4 0.48 0.56 0.72 0.8 0.96 1.
// Expected Cumulative Probability EF =
// 0.1
// 0.2
// 0.3
// 0.4
// 0.5
// 0.6
// 0.7
// 0.8
// 0.9
// 1.
// Calculated difference absolute value D =
// 10^(-8) *
//
// 2000000.
// 0.
// 6000000.
// 0.
// 2000000.
// 4000000.
// 2000000.
// 1.110D-08
// 6000000.
// 1.110D-08
// Theoretical table value for a significance level of 0.05=
// 0.27
// Since Dcal is less than the table value Dn accept the null hypothesis Ho
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