% Section 7.5 from book.        barnett 2/27/06

% plot the chi-squared pdf for different m = degrees of freedom...
w = 0:0.1:20;
figure;
plot(w, [chi2pdf(w,1); chi2pdf(w,2); chi2pdf(w,5); chi2pdf(w,10)], '-');
legend('1', '2', '5', '10'); title('Chi-squared pdf');
xlabel w; ylabel('f_{\chi^2}(w, v)'); axis([0 15 0 0.6]);

% look up w-values which fall on 2.5% and 97.5% percentiles of chi-squared...
n = 4;
alpha = 0.05;
a = chi2inv(alpha/2, n-1)
b = chi2inv(1-alpha/2, n-1)

% find a confidence interval on variance, given data with eg S^2 = 5.
S = sqrt(5);
disp(sprintf('95%% Conf Int on variance: [%f, %f]', (n-1)*S^2/b, (n-1)*S^2/a));