How can I fit a gaussian curve in python?

Question

I'm given an array and when I plot it I get a gaussian shape with some noise. I want to fit the gaussian. This is what I already have but when I plot this I do not get a fitted gaussian, instead I just get a straight line. I've tried this many different ways and I just can't figure it out.

random_sample=norm.rvs(h)

parameters = norm.fit(h)

fitted_pdf = norm.pdf(f, loc = parameters[0], scale = parameters[1])

normal_pdf = norm.pdf(f)

plt.plot(f,fitted_pdf,"green")
plt.plot(f, normal_pdf, "red")
plt.plot(f,h)
plt.show()

Answer 1

You can use fit from scipy.stats.norm as follows:

import numpy as np
from scipy.stats import norm
import matplotlib.pyplot as plt

data = np.random.normal(loc=5.0, scale=2.0, size=1000)
mean,std=norm.fit(data)

norm.fit tries to fit the parameters of a normal distribution based on the data. And indeed in the example above mean is approximately 5 and std is approximately 2.

In order to plot it, you can do:

plt.hist(data, bins=30, density=True)
xmin, xmax = plt.xlim()
x = np.linspace(xmin, xmax, 100)
y = norm.pdf(x, mean, std)
plt.plot(x, y)
plt.show()

The blue boxes are the histogram of your data, and the green line is the Gaussian with the fitted parameters.

Answer 2

There are many ways to fit a gaussian function to a data set. I often use astropy when fitting data, that's why I wanted to add this as additional answer.

I use some data set that should simulate a gaussian with some noise:

import numpy as np
from astropy import modeling

m = modeling.models.Gaussian1D(amplitude=10, mean=30, stddev=5)
x = np.linspace(0, 100, 2000)
data = m(x)
data = data + np.sqrt(data) * np.random.random(x.size) - 0.5
data -= data.min()
plt.plot(x, data)

Then fitting it is actually quite simple, you specify a model that you want to fit to the data and a fitter:

fitter = modeling.fitting.LevMarLSQFitter()
model = modeling.models.Gaussian1D()   # depending on the data you need to give some initial values
fitted_model = fitter(model, x, data)

And plotted:

plt.plot(x, data)
plt.plot(x, fitted_model(x))

---

However you can also use just Scipy but you have to define the function yourself:

from scipy import optimize

def gaussian(x, amplitude, mean, stddev):
    return amplitude * np.exp(-((x - mean) / 4 / stddev)**2)

popt, _ = optimize.curve_fit(gaussian, x, data)

This returns the optimal arguments for the fit and you can plot it like this:

plt.plot(x, data)
plt.plot(x, gaussian(x, *popt))