I\'m trying to fit the distribution of some experimental values with a custom probability density function. Obviously, the integral of the resulting function should always b
If you are able normalise your probability fitting function in advance then you can use this information to constrain your fit. A very simple example of this would be fitting a Gaussian to data. If one were to fit the following three-parameter (A, mu, sigma) Gaussian then it would be unnormalised in general:

however, if one instead enforces the normalisation condition on A:

then the Gaussian is only two parameter and is automatically normalised.