%Stat 351 Lecture 10
%Normal probability plot

X =[-0.4326
   -1.6656
    0.1253
    0.2877
   -1.1465
    1.1909
    1.1892
   -0.0376
    0.3273
    0.1746]

cdfplot(X)
hold on
plot([-2:0.1:2],normcdf([-2:0.1:2]),'r-')

>>H = lillietest(X,0.05)
H =
     0  %can't reject H_0 reject H_0 if H =1

>>orderedX = sort(X)
>>empirical = [1:10]'/10
empirical =

    0.1000
    0.2000
    0.3000
    0.4000
    0.5000
    0.6000
    0.7000
    0.8000
    0.9000
    1.0000

>>quantile = norminv(empirical,0,1)
quantile =
   -1.2816
   -0.8416
   -0.5244
   -0.2533
         0
    0.2533
    0.5244
    0.8416
    1.2816
       Inf %can't plot infinity


>>empirical = [1:10]'/11
>>quantile = norminv(empirical,0,1);
>>[quantile orderedX]
ans =

   -1.3352   -1.6656
   -0.9085   -1.1465
   -0.6046   -0.4326
   -0.3488   -0.0376
   -0.1142    0.1253
    0.1142    0.1746
    0.3488    0.2877
    0.6046    0.3273
    0.9085    1.1892
    1.3352    1.1909
>>plot(quantile,orderedX,'.')
>>hold on
>>plot(-2,-2,2,2)

>>A= chi2rnd(1,10000,1);
>>qqplot(A)
>>B=unifrnd(-10,10,10000,1)
>>qqplot(A,B)