Empirical Cumulative Distribution Function

In [1]:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from mpl_toolkits.basemap import Basemap
%matplotlib inline
import warnings
warnings.filterwarnings('ignore')
%config InlineBackend.figure_format = 'retina'

In [5]:

iris = pd.read_csv("https://raw.githubusercontent.com/uiuc-cse/data-fa14/gh-pages/data/iris.csv")

In [6]:

iris.head()

Out[6]:

	sepal_length	sepal_width	petal_length	petal_width	species
0	5.1	3.5	1.4	0.2	setosa
1	4.9	3.0	1.4	0.2	setosa
2	4.7	3.2	1.3	0.2	setosa
3	4.6	3.1	1.5	0.2	setosa
4	5.0	3.6	1.4	0.2	setosa

In [10]:

iris.shape[0]

Out[10]:

150

In [8]:

plt.hist(iris["petal_length"])

Out[8]:

(array([ 37.,  13.,   0.,   3.,   8.,  26.,  29.,  18.,  11.,   5.]),
 array([ 1.  ,  1.59,  2.18,  2.77,  3.36,  3.95,  4.54,  5.13,  5.72,
         6.31,  6.9 ]),
 <a list of 10 Patch objects>)

Square root rule¶

Normally people use the square root of the sample as a bin size

In [12]:

plt.hist(iris["petal_length"],bins=int(np.sqrt(iris.shape[0])))

Out[12]:

(array([ 23.,  27.,   0.,   0.,   3.,   8.,  18.,  25.,  18.,  17.,   7.,
          4.]),
 array([ 1.        ,  1.49166667,  1.98333333,  2.475     ,  2.96666667,
         3.45833333,  3.95      ,  4.44166667,  4.93333333,  5.425     ,
         5.91666667,  6.40833333,  6.9       ]),
 <a list of 12 Patch objects>)

Swarm plot¶

In [13]:

sns.swarmplot(x = "species", y = "petal_length", data = iris)

Out[13]:

<matplotlib.axes._subplots.AxesSubplot at 0x11ce6f550>

Empirical Cumulative Distributive function¶

In [14]:

def ecdf(data):
    """Compute ECDF for a one-dimensional array of measurements."""

    # Number of data points: n
    n = len(data)

    # x-data for the ECDF: x
    x = np.sort(data)

    # y-data for the ECDF: y
    y = np.arange(1, n+1) / n

    return x, y

ECDF plot for petal length¶

In [16]:

x,y = ecdf(iris["petal_length"])

In [24]:

plt.plot(x,y, marker = '.', linestyle = 'none')
plt.margins(0.02)
plt.xlabel('petal length (cm)')
plt.ylabel("ECDF")

Out[24]:

<matplotlib.text.Text at 0x11e7d9978>