Distribution Plots¶

Let's discuss some plots that allow us to visualize the distribution of a data set. These plots are:

  • distplot
  • jointplot
  • pairplot
  • rugplot
  • kdeplot

Imports¶

In [2]:
import seaborn as sns
%matplotlib inline

Data¶

Seaborn comes with built-in data sets!

In [3]:
tips = sns.load_dataset('tips')
In [4]:
tips.head()
Out[4]:
total_bill tip sex smoker day time size
0 16.99 1.01 Female No Sun Dinner 2
1 10.34 1.66 Male No Sun Dinner 3
2 21.01 3.50 Male No Sun Dinner 3
3 23.68 3.31 Male No Sun Dinner 2
4 24.59 3.61 Female No Sun Dinner 4

distplot¶

The distplot shows the distribution of a univariate set of observations.

In [16]:
sns.distplot(tips['total_bill'])
# Safe to ignore warnings

/Users/marci/anaconda/lib/python3.5/site-packages/statsmodels/nonparametric/kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j
Out[16]:
<matplotlib.axes._subplots.AxesSubplot at 0x11dd8e5f8>

To remove the kde layer and just have the histogram use:

In [9]:
sns.distplot(tips['total_bill'],kde=False,bins=30)
Out[9]:
<matplotlib.axes._subplots.AxesSubplot at 0x11c7b8668>

jointplot¶

jointplot() allows you to basically match up two distplots for bivariate data. With your choice of what kind parameter to compare with:

  • “scatter”
  • “reg”
  • “resid”
  • “kde”
  • “hex”
In [12]:
sns.jointplot(x='total_bill',y='tip',data=tips,kind='scatter')
Out[12]:
<seaborn.axisgrid.JointGrid at 0x11cfb28d0>
In [15]:
sns.jointplot(x='total_bill',y='tip',data=tips,kind='hex')
Out[15]:
<seaborn.axisgrid.JointGrid at 0x11d96f160>
In [17]:
sns.jointplot(x='total_bill',y='tip',data=tips,kind='reg')

/Users/marci/anaconda/lib/python3.5/site-packages/statsmodels/nonparametric/kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j
Out[17]:
<seaborn.axisgrid.JointGrid at 0x11e0cfba8>

pairplot¶

pairplot will plot pairwise relationships across an entire dataframe (for the numerical columns) and supports a color hue argument (for categorical columns).

In [18]:
sns.pairplot(tips)
Out[18]:
<seaborn.axisgrid.PairGrid at 0x11e844208>
In [21]:
sns.pairplot(tips,hue='sex',palette='coolwarm')
Out[21]:
<seaborn.axisgrid.PairGrid at 0x11ff7a828>

rugplot¶

rugplots are actually a very simple concept, they just draw a dash mark for every point on a univariate distribution. They are the building block of a KDE plot:

In [22]:
sns.rugplot(tips['total_bill'])
Out[22]:
<matplotlib.axes._subplots.AxesSubplot at 0x1207c8b70>

kdeplot¶

kdeplots are Kernel Density Estimation plots. These KDE plots replace every single observation with a Gaussian (Normal) distribution centered around that value. For example:

In [35]:
# Don't worry about understanding this code!
# It's just for the diagram below
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

#Create dataset
dataset = np.random.randn(25)

# Create another rugplot
sns.rugplot(dataset);

# Set up the x-axis for the plot
x_min = dataset.min() - 2
x_max = dataset.max() + 2

# 100 equally spaced points from x_min to x_max
x_axis = np.linspace(x_min,x_max,100)

# Set up the bandwidth, for info on this:
url = 'http://en.wikipedia.org/wiki/Kernel_density_estimation#Practical_estimation_of_the_bandwidth'

bandwidth = ((4*dataset.std()**5)/(3*len(dataset)))**.2


# Create an empty kernel list
kernel_list = []

# Plot each basis function
for data_point in dataset:
    
    # Create a kernel for each point and append to list
    kernel = stats.norm(data_point,bandwidth).pdf(x_axis)
    kernel_list.append(kernel)
    
    #Scale for plotting
    kernel = kernel / kernel.max()
    kernel = kernel * .4
    plt.plot(x_axis,kernel,color = 'grey',alpha=0.5)

plt.ylim(0,1)
Out[35]:
(0, 1)
In [37]:
# To get the kde plot we can sum these basis functions.

# Plot the sum of the basis function
sum_of_kde = np.sum(kernel_list,axis=0)

# Plot figure
fig = plt.plot(x_axis,sum_of_kde,color='indianred')

# Add the initial rugplot
sns.rugplot(dataset,c = 'indianred')

# Get rid of y-tick marks
plt.yticks([])

# Set title
plt.suptitle("Sum of the Basis Functions")
Out[37]:
<matplotlib.text.Text at 0x121c41da0>

So with our tips dataset:

In [41]:
sns.kdeplot(tips['total_bill'])
sns.rugplot(tips['total_bill'])

/Users/marci/anaconda/lib/python3.5/site-packages/statsmodels/nonparametric/kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j
Out[41]:
<matplotlib.axes._subplots.AxesSubplot at 0x121b82c50>
In [42]:
sns.kdeplot(tips['tip'])
sns.rugplot(tips['tip'])

/Users/marci/anaconda/lib/python3.5/site-packages/statsmodels/nonparametric/kdetools.py:20: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  y = X[:m/2+1] + np.r_[0,X[m/2+1:],0]*1j
Out[42]:
<matplotlib.axes._subplots.AxesSubplot at 0x12252cfd0>

Great Job!¶