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 2 and std is approximately 5.

In order to plot it, you can do:

plt.hist(data, bins=30, normed=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))

Answer 3

You can also fit an Gaussian function with curve_fit from scipy.optimize() where you can define your own customized function. Here, I am giving an example for a gaussian curve fitting. For example, if you have two arrays x and y.

from scipy.optimize import curve_fit
from scipy import asarray as ar,exp

x = ar(range(10))
y = ar([0,1,2,3,4,5,4,3,2,1])

n = len(x)                          #the number of data
mean = sum(x*y)/n                   #note this correction
sigma = sum(y*(x-mean)**2)/n        #note this correction

def gaus(x,a,x0,sigma):
    return a*exp(-(x-x0)**2/(2*sigma**2))

popt,pcov = curve_fit(gaus,x,y,p0=[1,mean,sigma])

plt.plot(x,y,'b+:',label='data')
plt.plot(x,gaus(x,*popt),'ro:',label='fit')
plt.legend()

The curve_fit function needs to be called with three arguments: the function that you want to fit (gaus() in this case), the values of the independent variable (in our case x), and the values of the depenedent variable (in our case y). The curve_fit funtion than returns an array with the optimal parameters (in a least squares sense) and a second array containing the covariance of the optimal parameters (more on that later).

Following is the output of the fit.