python - how to find area under curve?

Question

would like to ask if it is possible to calculate the area under curve for a fitted distribution curve?

The curve would look like this

I've seen some post online regarding the usage of trapz, but i'm not sure if it will work for a curve like that. Please enlighten me and thank you for the help!

Solution 1

If your distribution, f, is discretized on a set of points, x, that you know about, then you can use scipy.integrate.trapz or scipy.integrate.simps directly (pass f, x as arguments in that order). For a quick check (e.g. that your distribution is normalized), just sum the values of f and multiply by the grid spacing:

import numpy as np
from scipy.integrate import trapz, simps

x, dx = np.linspace(-100, 250, 50, retstep=True)
mean, sigma = 90, 20
f = np.exp(-((x-mean)/sigma)**2/2) / sigma / np.sqrt(2 * np.pi)
print('{:18.16f}'.format(np.sum(f)*dx))
print('{:18.16f}'.format(trapz(f, x)))
print('{:18.16f}'.format(simps(f, x)))

Output:

1.0000000000000002
0.9999999999999992
1.0000000000000016

Solution 2

Firstly, you have to find a function from a graph. You can check here. Then you can use integration in python with scipy. You can check here for integration. It is just math stuff as Daniel Sanchez says.