# Fit - first derivative **at limit**

Hello,
in performing a fit I obtain that for one of the parameter the first derivative is at limit.

EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 h1 1.09812e+02 3.60116e+00 2.30786e-03 -2.08599e-05
2 c1 1.86486e-02 fixed
3 s1 4.80290e-01 1.49304e-02 1.13552e-04 -6.63830e-05
4 h2 3.05939e+01 2.36242e+00 3.03778e-05 1.14984e-03
5 c2 1.64865e+00 fixed
6 s2 4.49226e-01 3.98833e-02 5.75048e-05 1.06085e-04
7 h3 7.38107e+00 1.92092e+00 4.02794e-05 2.75496e-03
8 c3 2.60808e+00 1.88809e-01 2.27532e-04 7.92311e-04
9 s3 5.72634e-01 1.08479e-01 9.98010e-04** at limit **

What does mean this result in term of the fit? Are the values obtained meaningful? How can I solve this problem?

Maria

ROOT Version: Not Provided
Platform: Not Provided
Compiler: Not Provided

@swunsch Can you help?

Hi!

I think what we see here is an output from minuit, which says that the respective parameter was at the limit at the minimum. That means that the minimum and error estimate is not reliable. See the documentation here, page 29 should be the correct source.

But let’s pull in @moneta as the actual expert

Best
Stefan

Yes, what I am doing is applying a minut procedure. The global response (chi-square, matrix error …) is good. I receive only this warning in the first derivative, so I was wondering if I can consider good the result for the parameter and not the respective error or both the parameter and the error are unreliable.
Maria

Hi,

Normally if a parameter is at the limit the fitted parameter value is reliable, this is the best value you can obtained given the provided bounds, but the error not.
A different procedure should be then used if reporting an error for that parameter is important. For example for lower bounded parameters, normally an upper limit is then reported and in that case a
different method is used (e.g. see asymptotic upper limit estimation performed in RooStats)

Best,

Lorenzo