Histogram fitting with python

Question

I've been surfing but haven't found the correct method to do the following.

I have a histogram done with matplotlib:

hist, bins, patches = plt.hist(distance, bins=100, normed='True')

From the plot, I can see that the distribution is more or less an exponential (Poisson distribution). How can I do the best fitting, taking into account my hist and bins arrays?

UPDATE

I am using the following approach:

x = np.float64(bins) # Had some troubles with data types float128 and float64
hist = np.float64(hist)
myexp=lambda x,l,A:A*np.exp(-l*x)
popt,pcov=opt.curve_fit(myexp,(x[1:]+x[:-1])/2,hist)

But I get

---> 41 plt.plot(stats.expon.pdf(np.arange(len(hist)),popt),'-')

ValueError: operands could not be broadcast together with shapes (100,) (2,)

Answer 1

What you described is a form of exponential distribution, and you want to estimate the parameters of the exponential distribution, given the probability density observed in your data. Instead of using non-linear regression method (which assumes the residue errors are Gaussian distributed), one correct way is arguably a MLE (maximum likelihood estimation).

scipy provides a large number of continuous distributions in its stats library, and the MLE is implemented with the .fit() method. Of course, exponential distribution is there:

In [1]:

import numpy as np
import scipy.stats as ss
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
#generate data 
X = ss.expon.rvs(loc=0.5, scale=1.2, size=1000)

#MLE
P = ss.expon.fit(X)
print P
(0.50046056920696858, 1.1442947648425439)
#not exactly 0.5 and 1.2, due to being a finite sample

In [3]:
#plotting
rX = np.linspace(0,10, 100)
rP = ss.expon.pdf(rX, *P)
#Yup, just unpack P with *P, instead of scale=XX and shape=XX, etc.
In [4]:

#need to plot the normalized histogram with `normed=True`
plt.hist(X, normed=True)
plt.plot(rX, rP)
Out[4]:

Your distance will replace X here.