Fit gamma distribution to histogram python

Your data does not appear to be gamma-distributed, but assuming it is, you could fit it like this:

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

gamma = stats.gamma
a, loc, scale = 3, 0, 2
size = 20000
y = gamma.rvs[a, loc, scale, size=size]

x = np.linspace[0, y.max[], 100]
# fit
param = gamma.fit[y, floc=0]
pdf_fitted = gamma.pdf[x, *param]
plt.plot[x, pdf_fitted, color='r']

# plot the histogram
plt.hist[y, normed=True, bins=30]

plt.show[]

• The area under the pdf [over the entire domain] equals 1. The area under the histogram equals 1 if you use normed=True.

• x has length size [i.e. 20000], and pdf_fitted has the same shape as x. If we call plot and specify only the y-values, e.g. plt.plot[pdf_fitted], then values are plotted over the x-range [0, size]. That is much too large an x-range. Since the histogram is going to use an x-range of [min[y], max[y]], we much choose x to span a similar range: x = np.linspace[0, y.max[]], and call plot with both the x- and y-values specified, e.g. plt.plot[x, pdf_fitted].

• As Warren Weckesser points out in the comments, for most applications you know the gamma distribution's domain begins at 0. If that is the case, use floc=0 to hold the loc parameter to 0. Without floc=0, gamma.fit will try to find the best-fit value for the loc parameter too, which given the vagaries of data will generally not be exactly zero.

I was surprised that I couldn't found this piece of code somewhere.

What I basically wanted was to fit some theoretical distribution to my graph. If you are lucky, you should see something like this:

from scipy import stats  
import numpy as np  
import matplotlib.pylab as plt

# create some normal random noisy data
ser = 50*np.random.rand[] * np.random.normal[10, 10, 100] + 20

# plot normed histogram
plt.hist[ser, normed=True]

# find minimum and maximum of xticks, so we know
# where we should compute theoretical distribution
xt = plt.xticks[][0]  
xmin, xmax = min[xt], max[xt]  
lnspc = np.linspace[xmin, xmax, len[ser]]

# lets try the normal distribution first
m, s = stats.norm.fit[ser] # get mean and standard deviation  
pdf_g = stats.norm.pdf[lnspc, m, s] # now get theoretical values in our interval  
plt.plot[lnspc, pdf_g, label="Norm"] # plot it

# exactly same as above
ag,bg,cg = stats.gamma.fit[ser]  
pdf_gamma = stats.gamma.pdf[lnspc, ag, bg,cg]  
plt.plot[lnspc, pdf_gamma, label="Gamma"]

# guess what :] 
ab,bb,cb,db = stats.beta.fit[ser]  
pdf_beta = stats.beta.pdf[lnspc, ab, bb,cb, db]  
plt.plot[lnspc, pdf_beta, label="Beta"]

plt.show[]  

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

#define x-axis values
x = np.linspace [0, 40, 100] 

#calculate pdf of Gamma distribution for each x-value
y = stats.gamma.pdf[x, a=5, scale=3]

#create plot of Gamma distribution
plt.plot[x, y]

#display plot
plt.show[]

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

#define three Gamma distributions
x = np.linspace[0, 40, 100]
y1 = stats.gamma.pdf[x, a=5, scale=3]
y2 = stats.gamma.pdf[x, a=2, scale=5]
y3 = stats.gamma.pdf[x, a=4, scale=2]

#add lines for each distribution
plt.plot[x, y1, label=shape=5, scale=3']
plt.plot[x, y2, label='shape=2, scale=5']
plt.plot[x, y3, label='shape=4, scale=2']

#add legend
plt.legend[]

#display plot
plt.show[]

How do you fit a gamma distribution?

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