How to Calculate Skewness and Kurtosis in Python?

Skewness is a statistical term and it is a way to estimate or measure the shape of a distribution.  It is an important statistical methodology that is used to estimate the asymmetrical behavior rather than computing frequency distribution. Skewness can be two types:

• Symmetrical: A distribution can be called symmetric if it appears the same from the left and right from the center point.
• Asymmetrical: A distribution can be called asymmetric if it doesn’t appear the same from the left and right from the center point.

Distribution on the basis of skewness value:

• Skewness = 0: Then normally distributed.
• Skewness > 0: Then more weight in the left tail of the distribution.
• Skewness < 0: Then more weight in the right tail of the distribution.

Kurtosis:

It is also a statistical term and an important characteristic of frequency distribution. It determines whether a distribution is heavy-tailed in respect of the normal distribution. It provides information about the shape of a frequency distribution.

• kurtosis for normal distribution is equal to 3.
• For a distribution having kurtosis < 3: It is called playkurtic.
• For a distribution having kurtosis > 3, It is called leptokurtic and it signifies that it tries to produce more outliers rather than the normal distribution.

This article focuses on how to Calculate Skewness & Kurtosis in Python.

How to Calculate Skewness & Kurtosis in Python?

Calculating Skewness and Kurtosis is a step-by-step process. The steps are discussed below.

Step 1: Importing SciPy library.

SciPy is an open-source scientific library. It provides inbuilt functions to calculate Skewness and Kurtosis. We can import this library by using the below code.

Python3

# Importing scipy
import scipy

Step 2: Create a dataset.

Before calculating Skewness and Kurtosis we need to create a dataset.

Python3

# Creating a dataset
dataset = [10, 25, 14, 26, 35, 45, 67, 90,
           40, 50, 60, 10, 16, 18, 20]

Step 3: Computing skewness of the dataset.

We can calculate the skewness of the dataset by using the inbuilt skew() function. Its syntax is given below,

Syntax:

scipy.stats.skew(array, axis=0, bias=True)

Parameters:

• array: It represents the input array (or object) containing elements.
• axis: It signifies the axis along which we want to find the skewness value (By default axis = 0).
• bias = False: Calculations are corrected to statistical bias.

Return Type:

Skewness value of the data set, along the axis.

Example:

Python3

# Importing library
from scipy.stats import skew

# Creating a dataset
dataset = [88, 85, 82, 97, 67, 77, 74, 86,
           81, 95, 77, 88, 85, 76, 81]

# Calculate the skewness
print(skew(dataset, axis=0, bias=True))

Output:

skewness of the dataset

It signifies that the distribution is positively skewed

Step 4: Computing kurtosis of the dataset.

We can calculate the kurtosis of the dataset by using the inbuilt kurtosis() function. Its syntax is given below,

Syntax:

scipy.stats.kurtosis(array, axis=0, fisher=True, bias=True)

Parameters:

• array: Input array or object having the elements.
• axis: It represents the axis along which the kurtosis value is to be measured. By default axis = 0.
• fisher = True: The fisher’s definition will be used (normal 0.0).
• fisher =  False: The Pearson’s definition will be used (normal 3.0).
• Bias = True: Calculations are corrected for statistical bias, if set to False.

Return Type:

Kurtosis value of the normal distribution for the data set.

Example:

Python3

# Importing library

from scipy.stats import kurtosis

# Creating a dataset
dataset = [88, 85, 82, 97, 67, 77, 74, 86,
           81, 95, 77, 88, 85, 76, 81]


# Calculate the kurtosis
print(kurtosis(dataset, axis=0, bias=True))

Output:

kurtosis of the dataset

It signifies that the distribution has more values in the tails compared to a normal distribution.