How do I put a constraint on SciPy curve fit?

Question

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

Answer 1

You could ensure that your fitted probability distribution is normalised via a numerical integration. For example, assuming that you have data x and y and that you have defined an unnormalised_function(x, a, b) with parameters a and b for your probability distribution, which is defined on the interval x1 to x2 (which could be infinite):

from scipy.optimize import curve_fit
from scipy.integrate import quad

# Define a numerically normalised function
def normalised_function(x, a, b):
    normalisation, _ = quad(lambda x: unnormalised_function(x, a, b), x1, x2)
    return unnormalised_function(x, a, b)/normalisation

# Do the parameter fitting
fitted_parameters, _ = curve_fit(normalised_function, x, y)