Plotting CDF of a pandas series in python

Question

Is there a way to do this? I cannot seem an easy way to interface pandas series with plotting a CDF.

Answer 1

I believe the functionality you're looking for is in the hist method of a Series object which wraps the hist() function in matplotlib

Here's the relevant documentation

In [10]: import matplotlib.pyplot as plt  In [11]: plt.hist? ... Plot a histogram.  Compute and draw the histogram of *x*. The return value is a tuple (*n*, *bins*, *patches*) or ([*n0*, *n1*, ...], *bins*, [*patches0*, *patches1*,...]) if the input contains multiple data. ... cumulative : boolean, optional, default : False     If `True`, then a histogram is computed where each bin gives the     counts in that bin plus all bins for smaller values. The last bin     gives the total number of datapoints.  If `normed` is also `True`     then the histogram is normalized such that the last bin equals 1.     If `cumulative` evaluates to less than 0 (e.g., -1), the direction     of accumulation is reversed.  In this case, if `normed` is also     `True`, then the histogram is normalized such that the first bin     equals 1.  ... 

For example

In [12]: import pandas as pd  In [13]: import numpy as np  In [14]: ser = pd.Series(np.random.normal(size=1000))  In [15]: ser.hist(cumulative=True, density=1, bins=100) Out[15]: <matplotlib.axes.AxesSubplot at 0x11469a590>  In [16]: plt.show() 

Answer 2

In case you are also interested in the values, not just the plot.

import pandas as pd  # If you are in jupyter %matplotlib inline 

This will always work (discrete and continuous distributions)

# Define your series s = pd.Series([9, 5, 3, 5, 5, 4, 6, 5, 5, 8, 7], name = 'value') df = pd.DataFrame(s) 

# Get the frequency, PDF and CDF for each value in the series  # Frequency stats_df = df \ .groupby('value') \ ['value'] \ .agg('count') \ .pipe(pd.DataFrame) \ .rename(columns = {'value': 'frequency'})  # PDF stats_df['pdf'] = stats_df['frequency'] / sum(stats_df['frequency'])  # CDF stats_df['cdf'] = stats_df['pdf'].cumsum() stats_df = stats_df.reset_index() stats_df 

# Plot the discrete Probability Mass Function and CDF. # Technically, the 'pdf label in the legend and the table the should be 'pmf' # (Probability Mass Function) since the distribution is discrete.  # If you don't have too many values / usually discrete case stats_df.plot.bar(x = 'value', y = ['pdf', 'cdf'], grid = True) 

Alternative example with a sample drawn from a continuous distribution or you have a lot of individual values:

# Define your series s = pd.Series(np.random.normal(loc = 10, scale = 0.1, size = 1000), name = 'value') 

# ... all the same calculation stuff to get the frequency, PDF, CDF 

# Plot stats_df.plot(x = 'value', y = ['pdf', 'cdf'], grid = True) 

For continuous distributions only

Please note if it is very reasonable to make the assumption that there is only one occurence of each value in the sample (typically encountered in the case of continuous distributions) then the groupby() + agg('count') is not necessary (since the count is always 1).

In this case, a percent rank can be used to get to the cdf directly.

Use your best judgment when taking this kind of shortcut! :)

# Define your series s = pd.Series(np.random.normal(loc = 10, scale = 0.1, size = 1000), name = 'value') df = pd.DataFrame(s) 

# Get to the CDF directly df['cdf'] = df.rank(method = 'average', pct = True) 

# Sort and plot df.sort_values('value').plot(x = 'value', y = 'cdf', grid = True)