Chi-square and F distributions when degrees of freedom tends to infinity #203
Description
A year ago I opened the bug https://savannah.gnu.org/bugs/?66034 about inconsistent results of finv() when the second degrees of freedom parameter tends to infinity. The bug was confirmed and solved. Now I can see that theproblem is present in other functions that finv() and also in chi-square distribution. I present here some example results
fpdf() in Matlab:
>> fpdf(2,4,Inf)
ans =
0.1465
>> fpdf(2,Inf,4)
ans =
0.1839
>> fpdf(2,Inf,Inf)
ans =
0
fpdf() in Octave:
>> fpdf(2,4,Inf)
ans = NaN
>> fpdf(2,Inf,4)
ans = NaN
>> fpdf(2,Inf,Inf)
ans = NaN
fcdf() produces the same results in Octave and Matlab, as well as finv()
finv() works for Inf in DF2, but not for DF1 and DF1 and DF2 simultaneously. finv() in Matlab:
>> finv(0.35,Inf,4)
ans =
0.9014
>> finv(0.35,Inf,Inf)
ans =
1
finv() in Octave:
>> finv(0.35,Inf,4)
ans = NaN
>> finv(0.35,Inf,Inf)
ans = NaN
chi2pdf() in Matlab:
>> chi2pdf(2,Inf)
ans =
0
chi2pdf() in Octave:
>> chi2pdf(2,Inf)
ans = NaN
chi2cdf() works well in both Octave and Matlab.
chi2inv() gets NaN for DF=Inf in both Octave and Matlab:
>> chi2inv(0.35,Inf)
ans =
NaN
>> chi2inv(0.35,Inf)
ans = NaN
If we introduce a high value instead of Inf in Octave, the results are equal as in Matlab, but from a value onwards the behavior is erratic
>> fpdf(2,4,10000000000000000)
ans = 2.3515e-05
>> fpdf(2,4,1000000000000000)
ans = 1.4790
>> fpdf(2,4,100000000000000)
ans = 0.1349
>> fpdf(2,4,10000000000000)
ans = 0.1447
>> fpdf(2,4,1000000000000)
ans = 0.1467
>> fpdf(2,4,100000000000)
ans = 0.1465
>> fpdf(2,4,10000000000)
ans = 0.1465
>> fpdf(2,4,1000000000)
ans = 0.1465
>> fpdf(2,4,100000000)
ans = 0.1465
>> fpdf(2,4,10000000)
ans = 0.1465
>> fpdf(2,4,1000000)
ans = 0.1465
>> fpdf(2,4,100000)
ans = 0.1465
>> fpdf(2,4,10000)
ans = 0.1466