I want to create a CDF with NumPy, my code is the next:

``````histo = np.zeros(4096, dtype = np.int32)
for x in range(0, width):
for y in range(0, height):
histo[data[x][y]] += 1
q = 0
cdf = list()
for i in histo:
q = q + i
cdf.append(q)
``````

I am walking by the array but take a long time the program execution. There is a built function with this feature, isn’t?

Using a histogram is one solution but it involves binning the data. This is not necessary for plotting a CDF of empirical data. Let `F(x)` be the count of how many entries are less than `x` then it goes up by one, exactly where we see a measurement. Thus, if we sort our samples then at each point we increment the count by one (or the fraction by 1/N) and plot one against the other we will see the “exact” (i.e. un-binned) empirical CDF.

A following code sample demonstrates the method

``````import numpy as np
import matplotlib.pyplot as plt

N = 100
Z = np.random.normal(size = N)
# method 1
H,X1 = np.histogram( Z, bins = 10, normed = True )
dx = X1 - X1
F1 = np.cumsum(H)*dx
#method 2
X2 = np.sort(Z)
F2 = np.array(range(N))/float(N)

plt.plot(X1[1:], F1)
plt.plot(X2, F2)
plt.show()
``````

It outputs the following I’m not really sure what your code is doing, but if you have `hist` and `bin_edges` arrays returned by `numpy.histogram` you can use `numpy.cumsum` to generate a cumulative sum of the histogram contents.

``````>>> import numpy as np
>>> hist, bin_edges = np.histogram(np.random.randint(0,10,100), normed=True)
>>> bin_edges
array([ 0. ,  0.9,  1.8,  2.7,  3.6,  4.5,  5.4,  6.3,  7.2,  8.1,  9. ])
>>> hist
array([ 0.14444444,  0.11111111,  0.11111111,  0.1       ,  0.1       ,
0.14444444,  0.14444444,  0.08888889,  0.03333333,  0.13333333])
>>> np.cumsum(hist)
array([ 0.14444444,  0.25555556,  0.36666667,  0.46666667,  0.56666667,
0.71111111,  0.85555556,  0.94444444,  0.97777778,  1.11111111])
``````

update for numpy version 1.9.0. user545424’s answer does not work in 1.9.0. This works:

``````>>> import numpy as np
>>> arr = np.random.randint(0,10,100)
>>> hist, bin_edges = np.histogram(arr, density=True)
>>> hist = array([ 0.16666667,  0.15555556,  0.15555556,  0.05555556,  0.08888889,
0.08888889,  0.07777778,  0.04444444,  0.18888889,  0.08888889])
>>> hist
array([ 0.1       ,  0.11111111,  0.11111111,  0.08888889,  0.08888889,
0.15555556,  0.11111111,  0.13333333,  0.1       ,  0.11111111])
>>> bin_edges
array([ 0. ,  0.9,  1.8,  2.7,  3.6,  4.5,  5.4,  6.3,  7.2,  8.1,  9. ])
>>> np.diff(bin_edges)
array([ 0.9,  0.9,  0.9,  0.9,  0.9,  0.9,  0.9,  0.9,  0.9,  0.9])
>>> np.diff(bin_edges)*hist
array([ 0.09,  0.1 ,  0.1 ,  0.08,  0.08,  0.14,  0.1 ,  0.12,  0.09,  0.1 ])
>>> cdf = np.cumsum(hist*np.diff(bin_edges))
>>> cdf
array([ 0.15,  0.29,  0.43,  0.48,  0.56,  0.64,  0.71,  0.75,  0.92,  1.  ])
>>>
``````

To complement Dan’s solution.
In the case where there are several identical values in your sample, you can use numpy.unique :

``````Z = np.array([1,1,1,2,2,4,5,6,6,6,7,8,8])
X, F = np.unique(Z, return_index=True)
F=F/X.size

plt.plot(X, F)
``````

I am not sure if there is a ready-made answer, the exact thing to do is to define a function like:

``````def _cdf(x,data):
return(sum(x>data))
``````

This will be pretty fast.