# Finding Kurtosis For A Pandas.series

## Overview:

• Kurtosis is a statistical measure that describes the peakedness of the curve of distribution. It is defined as the fourth central moment divided by the standard deviation.
• When the distribution is thin and tall it is called a Leptokurtic distribution.
• When the distribution is Leptokurtic both of the following things happen:
• Large number of small deviations from the mean
• Large number of large deviations from the mean
• In Investment, an asset with Leptokurtic returns can mean higher probability for extremely low or extremely high returns and associated higher value at risk.
• When the distribution is less peaked or flatter than the normal distribution, it is called Platykurtic distribution. In a Platykurtic distribution, the tail of the distribution is extremely thin with outliers less than that of the normal distribution.
• When the distribution is Mesokurtic the curve resembles that of a normal distribution curve.

## Finding Kurtosis for a pandas Series:

• The class Series from the Python library pandas implements a one-dimensional collection with several statistical and mathematical functions for Data Analysis.
• Series.kurtosis() function computes the Fisher’s kurtosis or Excess Kurtosis for the data present in the series. As per Fisher’s kurtosis - A leptokurtic distribution has a Kurtosis value greater than 0, a normal distribution or a mesokurtic distribution has a Kurtosis value of 0 and a Platykurtic distribution has a Kurtosis value smaller than 0. Kurtosis can be calculated for pandas.DataFrame columns and rows as well.

## Example 1:

The Fisher’s Kurtosis value found for the pandas.Series instance in this example is greater than 0 and hence the distribution present in the Series is Leptokurtic.

 # Python example program to compute kurtosis of # the distribution represented by a pandas.Series import pandas as pds   # Percentage returns from the investment on an asset returns = [3,3,10,3,5,4,5,10,4];   # Create pandas.Series instance series  = pds.Series(returns);   print("Kurtosis:"); print(round(series.kurtosis(), 2));

## Output:

 Kurtosis: 0.18

## Example 2:

The Fisher’s Kurtosis value found for the pandas.Series instance in this example is less than 0 and hence the distribution present in the Series is Platykurtic.

 # Python example program to compute kurtosis of # the distribution represented by a pandas.Series import pandas as pds   # Values of a distribution vals = [2,2.2,2.3,2.1,1.9,2.3];   # Create pandas.Series instance series  = pds.Series(vals);   print("Kurtosis:"); print(round(series.kurtosis(), 2));

## Output:

 Kurtosis: -1.48