bsp_5_3.m

% Beispiel für Kap 5.3
%% Beispiel Saurer Regen
xi = [4.9387 4.8816 5.2655 5.2952 1.6869 4.9456 5.1463 5.2094 5.2547 ...
      4.7760 5.1551 4.6190 4.9984 5.4597 5.0853 4.7238]
n = length(xi);
p = 0.5;
m0 = 5.2;

Tx = sum(xi < 5.2)
pW = 1 - binocdf(Tx-1, n, p)

%% Lebensdauer Festplatten
X = [6.9175, 7.1546, 8.0619, 6.7216, 7.6289, 8.2784];
Y = [7.0103, 6.1237, 6.0309, 7.4330, 6.8247];
n = length(X);
m = length(Y);

lebensdauer = [X, Y];
typ = [ones(1,n), 2*ones(1,m)];
[wert,idx] = sort(lebensdauer);
herst = typ(idx);
rang = 1:(n+m);
fprintf('Rang   Wert   Hersteller\n')
fprintf(' %2d   %6.4f      %1d\n', [rang; wert; herst])

T = sum(rang(herst == 1))

c1 = ranksumcdf(T,n,m)
c2 = ranksumcdf(T-1,n,m)
pW = 2*min(c1, 1-c2)

%% 5.3 Mendels Erbsen
pj = [9,3,3,1]/16;
Nj = [315, 101, 108, 32];
n = sum(Nj);
T = sum((Nj - n*pj).^2./(n*pj))
z = chi2inv(1-0.05, 3)
pW = 1 - chi2cdf(T, 3)

%% 5.3 Schicht und Maschine
Nij = [12    14    13   12;
       16    13    15   11;
       11    10    9    19]
mj = sum(Nij)
ni = sum(Nij')'
n = sum(ni)
pi = ni/n
qj = mj/n
T = sum(sum((Nij - n*pi*qj).^2./(n*pi*qj)))
r = length(ni);
s = length(mj);
z = chi2inv(1-0.05, (r-1)*(s-1))
pW = 1 - chi2cdf(T, (r-1)*(s-1))

%% 5.3 Kolmogorov-Smirnov-Test
X0 = [4.9795 4.9359 4.9858 4.9968 5.0500 4.9599 5.0046 5.0137 4.8933 ...
      5.0202 4.9521 4.9837];
X = sort(X0);
n = length(X);
Fn = (1:n)/n;
mu = 5;
sigma = 0.05;
F0 = normcdf(X, mu, sigma);
do = abs(F0 - Fn);
du = abs(F0 - [0, Fn(1:n-1)]);

OUT = [(1:n)', X', Fn', F0', do', du'];
fprintf('i     xi     Fn(xi)  F0(xi)  d_i,o  d_i,u\n')
fprintf('%2d  %6.4f  %6.4f  %6.4f  %6.4f  %6.4f\n', OUT');

T = max([do, du])

% oder direkt mit STB-Funktion
[verwerfen, pWert, T, KS_al_n] = kstest((X0 - mu)/sigma)