#
# function gof(x)
#
# The function [qn,answer,lower,upper]=gof(x) implements a two-tail
# 5% significance test of uniformity based on the statistic Qn, in
# Fortiana and Grane (2002). H0 is the null hypothesis that the sample
# is uniformly distributed in [0,1]. For a sample size of 2<=n<=50
# the exact test is performed, while for n>50  the asymptotic test is
# performed.
#
# input: x is a column vector containing the sample.
#
# output: qn is the computed value of the test satistic,
#         answer is a string of characters: either "accept H0" or
#                "reject H0",
#         lower is the lower-tail critical value,
#         upper is the upper-tail critical value.
#
function [qn,answer,lower,upper]=gof(x)
# cv is a matrix containg the two-tail critical values
# for a 5% significance test.
cv=[0          0;        0.01887    1.26283;  0.12573    1.20760;
    0.24049    1.20177;  0.33397    1.20121;  0.40709    1.19460;
    0.46459    1.18852;  0.51056    1.18321;  0.54796    1.17819;
    0.57894    1.17350;  0.60502    1.16915;  0.62730    1.16513;
    0.64658    1.16139;  0.66346    1.15790;  0.67837    1.15463;
    0.69166    1.15158;  0.70359    1.14870;  0.71437    1.14600;
    0.72416    1.14345;  0.73310    1.14103;  0.74131    1.13875;
    0.74887    1.13657;  0.75586    1.13451;  0.76235    1.13254;
    0.76839    1.13066;  0.77403    1.12887;  0.77931    1.12715;
    0.78427    1.12550;  0.78894    1.12392;  0.79334    1.12240;
    0.79750    1.12095;  0.80143    1.11954;  0.80516    1.11819;
    0.80871    1.11688;  0.81208    1.11562;  0.81530    1.11441;
    0.81836    1.11323;  0.82129    1.11209;  0.82409    1.11099;
    0.82678    1.10992;  0.82935    1.10888;  0.83182    1.10788;
    0.83420    1.10690;  0.83648    1.10595;  0.83867    1.10503;
    0.84079    1.10413;  0.84283    1.10326;  0.84480    1.10241;
    0.84670    1.10158;  0.84854    1.10077];
#
# computing the Qn statistic
n=length(x);
x=sort(x);
a=zeros(n,1);
for i=1:n
   a(i,1)=(2*i-n-1);
end
qn=(6/n^2)*a'*x;
if n<=50
# performing the exact test
   lower=cv(n,1); upper=cv(n,2);
   # checking if Qn belongs to the exact critical region
   if qn<lower | qn>upper
      answer="reject H0";
   else
      answer="accept H0";
   endif
else
# performing the asymptotic test
   lower=-1.95996; upper=1.95996;
   # standardizing Qn
   m=(n-1)/n; s=sqrt(1/(5*n));
   qn=(qn-m)/s;
   # checking if the standardized Qn belongs to the
   # asymptotic critical region
   if qn<lower | qn>upper
      answer="reject H0";
   else
      answer="accept H0";
   endif
endif
endfunction