%Stat 351
% Kolmogorov Smirnov Test


>>X=[0.1:0.1:1]
X =
   0.1000  0.2000  0.3000  0.4000  0.5000  0.6000  0.7000  0.8000  0.9000  1.0000

>>cdfplot(X)
>>hold on

%Testing N(0.5,1) HW1 Problem 1.
>>Y=normrnd(0.5,1,1000,1);
>>cdfplot(Y);

>>normcdf(X,0.5,1)
ans =
    0.3446  0.3821  0.4207  0.4602  0.5000  0.5398  0.5793 0.6179  0.6554  0.6915


>>max(X-normcdf(X,0.5,1))
ans =
    0.3085

>>1.36/sqrt(10)
ans =
    0.4301

%Testing Unif(0,1)
>>max(X-unifcdf(X,0,1))
ans =
     0

%Using built-in function
>>[H,P]=kstest(X,[X',normcdf(X,0.5,1)'])
P =
    0.1466

>>[H,P] = kstest(X,[X',unifcdf(X,0,1)'])
P =
    0.9999

>>income =[9800
10200
9300
8700
15200
6900
8600
9600
12200
15500
11600
7200]

>>Z = (income-mean(income))/std(income)
Z =
   -0.2164
   -0.0721
   -0.3966
   -0.6130
    1.7308
   -1.2621
   -0.6491
   -0.2885
    0.6491
    1.8390
    0.4327
   -1.1539

>>[H,P]=kstest(Z,[Z,normcdf(Z,0,1)])
P =
    0.7002

>>[H,P]=lillietest(Z)
P =
   NaN    
%NaN returned when P is not in the inverval [0.01, 0.20].