# The FCN of simultaneous fit of two data samples

Dear All,
I have two data samples: data and data_ctl, I perform individual fits on data and data_ctl, I also perform a simutaneous fit on data and data_ctl;

My first problem is:

1. I use Likelihood method to fit data with model, fit data_ctl with model_ctl, and obtain the minimum FCN_1min and FCN_2min, respectively;
2. I use Likelihood method to simultaneously fit data with model and data_ctl with model_ctl, and obtain the FCN_min of the simultaneous fit; (in the simultaneous fit, the parameters of model and model_ctl are free);
3. I find FCN_min != FCN_1min + FCN_2min;
4. But, in mathematics, a simultaneously fit means to search the minmum value of FCN = FCN_1 + FCN_2; it should be FCN_min = FCN_1min + FCN_2min; because FCN_1min and FCN_2min are the minimum value of each part; the minimum value of FCN shoule be FCN_1min + FCN_2min, right?
the script is attached as: rf501_simultaneouspdf_likelihood.C

My second problem is:

1. I use Least-Chi2 method to fit data with model, fit data_ctl with model_ctl, and obtain the minimum FCN_1min and FCN_2min, respectively;
2. I use Least-Chi2 method to simultaneously fit data with model and data_ctl with model_ctl, and obtain the FCN_min of the simultaneous fit; (in the simultaneous fit, the parameters of model and model_ctl are free);
3. I find FCN_min = FCN_1min + FCN_2min, which is as the mathematical prediction;
4. However, when I use my real data, for Least-Chi2 method I find FCN_min != FCN_1min + FCN_2min,