Goodness of fit test for categorical data with non-negative real numbersca

An experiment that I conduct has 5 outcomes: A, B, C and D. I conduct 12 trials for this experiment. I observe, for example:

Outcome : Frequency
A : 2
B : 3
C : 0
D : 5
E : 2

Now, I have a model that predicts the frequency. However, the predictions are non-negative real numbers. For example:

Outcome : Predicted frequency
A : 1.75
B : 2.77
C : 0.11
D : 3.82
E : 3.55

I attempted to use the Pearson's Chi-square goodness of fit test to evaluate . However, since the values of frequency are below 5, I read that this test is not the best choice (= reliable). So, I attempted to use Fisher's exact test. The limitation of Fisher's exact test is that the data has to be non-negative integers.

My question: Is there a way to evaluate the p-value between the observed and predicted sets of data where the predicted data are not integers, but non-negative real numbers. The values of frequency are often lesser than 5.


TS Contributor
part of the problem is that in the measured dataset you do not have frequencies but the number of occurrences , in the prediction you have probably some kind of frequencies, though they do not sum to 100% . I guess the first step should be to unify the outputs of the experiments and the model and then see how you can compare them.