I have parameter estimates fitting a particular nonlinear model for thousands of experimental cycles. My goal is to find a nice way to tag those cycles which didn't fit the model very well. Currently I am comparing RMSE values for this. I have a huge list of RMSE values and am looking for a cutoff RMSE past which to flag it.
I plotted the histogram of RMSEs and found that they fit a log-normal distribution. However, I was informed that the proper distribution to use in this case is $\chi^2$. For my purposes the distribution I use doesn't seem to matter as long as it fits well, but since I was curious, I fitted a $\gamma$ distribution (which wikipedia informed me $\chi^2$ was a special case) to the RMSE histogram, but the parameters didn't seem to fit quite as well. Is the $\gamma$ distribution really that more meaningful?
Also, if you have any alternative suggestions for approaching my problem I would love to hear them.