numpy - Fit mixture of two gaussian/normal distributions to a histogram from one set of data, python

Question

I have one set of data in python. I am plotting this as a histogram, this plot shows a bimodal distribution, therefore I am trying to plot two gaussian profiles over each peak in the bimodality.

If i use the code below is requires me to have two datasets with the same size. however I just have one dataset, and this cannot be divided equally. How can I fit these two gaussians

from sklearn import mixture
import matplotlib.pyplot
import matplotlib.mlab
import numpy as np
clf = mixture.GMM(n_components=2, covariance_type='full')
clf.fit(yourdata)
m1, m2 = clf.means_
w1, w2 = clf.weights_
c1, c2 = clf.covars_
histdist = matplotlib.pyplot.hist(yourdata, 100, normed=True)
plotgauss1 = lambda x: plot(x,w1*matplotlib.mlab.normpdf(x,m1,np.sqrt(c1))[0], linewidth=3)
plotgauss2 = lambda x: plot(x,w2*matplotlib.mlab.normpdf(x,m2,np.sqrt(c2))[0], linewidth=3)
plotgauss1(histdist[1])
plotgauss2(histdist[1])

Answer 1

Here a simulation with scipy tools :

from pylab import *
from scipy.optimize import curve_fit

data=concatenate((normal(1,.2,5000),normal(2,.2,2500)))
y,x,_=hist(data,100,alpha=.3,label='data')

x=(x[1:]+x[:-1])/2 # for len(x)==len(y)

def gauss(x,mu,sigma,A):
    return A*exp(-(x-mu)**2/2/sigma**2)

def bimodal(x,mu1,sigma1,A1,mu2,sigma2,A2):
    return gauss(x,mu1,sigma1,A1)+gauss(x,mu2,sigma2,A2)

expected=(1,.2,250,2,.2,125)
params,cov=curve_fit(bimodal,x,y,expected)
sigma=sqrt(diag(cov))
plot(x,bimodal(x,*params),color='red',lw=3,label='model')
legend()
print(params,'
',sigma)    

The data is the superposition of two normal samples, the model a sum of Gaussian curves. we obtain :

And the estimate parameters are :

# via pandas :
# pd.DataFrame(data={'params':params,'sigma':sigma},index=bimodal.__code__.co_varnames[1:])
            params     sigma
mu1       0.999447  0.002683
sigma1    0.202465  0.002696
A1      226.296279  2.597628
mu2       2.003028  0.005036
sigma2    0.193235  0.005058
A2      117.823706  2.658789