function p = chitest(x,k)
% MS-E2170 Simulation
% Exercise 1.4: Chi-square test (Demo)
% function p = chitest(x,k)
% This function returns the p-value of the chi-square test
%
% ---------------------------------------------------------------
% INPUT
% x:       Observations (Nx1 double)
% k:       Number of sub intervals (1x1 double)
% ---------------------------------------------------------------
% OUTPUT
% p:       p-value of the chi-square test (1x1 double)
% ---------------------------------------------------------------
% Created:
% 2018-02-19 Heikki Puustinen


% First calculate the sample size.
N = length(x);

% The sub intervals of [0 1] are [(i-1)/k, i/k], i = 1,2,...,k. 
% To calculate the observed values within each sub interval:

% Initialize the variable where the number of occurrences are stored. 
f = zeros(k,1);

% Loop through sub intervals.
for ii = 1:k
    % Count how many xs are within the ii:th sub interval.
    f(ii) = sum(x > (ii-1)/k & x <= (ii/k));
end

% The test statistics:
X2 = sum((f - N/k).^2 ./ (N/k));

% The P-value of the test is the tail probability of the chi-square
% distribution at X2:
p = 1 - x2cdf(X2,k-1);