#Assessing critical value 
# on the basis of simulated distribution of the test statistic
# under fixed significance level (a) and sample size (n);
# ls - number of replication,

n=100
ls=10000
a=0.05
#H0: p=p0; H1: p=p1
czas=proc.time()
#chi-square test:
k=9
p0=matrix(0,k,1); 
#tested distribution:
for (i in 1:k) p0[i]=log10(1+1/i)
qs=matrix(0,ls,1)
ws=matrix(0,ls,1)

fitchi=function(n,p,w) 
{#evaluation of the test statistic
 n*sum((w-p)*(w-p)/p)}

bs=0; 
for (t in 1:ls) {ws=rmultinom(1,n,p0)/n; qs[t]=fitchi(n,p0,ws)}
qs=sort(qs)
wk=qs[floor((1-a)*ls)+1]

#sample size:
n
#simulated critical value:
wk;
#significance level:
a
proc.time()-czas
alarm()