Each Answer to this Q is separated by one/two green lines.

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[1] - X1[0]
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.