Pandas kurt() Function Tutorial (With Examples)

Introduction to kurt() Function

In data analysis and statistics, understanding the distribution of data is crucial. The kurt() function in the Pandas library is a useful tool for assessing the shape of a distribution by calculating its kurtosis. Kurtosis measures the tails and peaks of a distribution compared to a normal distribution. A positive kurtosis indicates heavier tails and a sharper peak, while negative kurtosis suggests lighter tails and a flatter peak.

In this tutorial, we will explore the kurt() function in Pandas, its syntax, parameters, and how to interpret its results. We will also provide practical examples to demonstrate its usage.

Table of Contents

1. Introduction to kurt() Function
2. Syntax of kurt() Function
3. Parameters of kurt() Function
4. Interpreting Kurtosis Values
5. Examples of Using kurt() Function

• Example 1: Analyzing Kurtosis of a Gaussian Distribution
• Example 2: Analyzing Kurtosis of a Real-World Dataset

1. Conclusion

Syntax of kurt() Function

The syntax of the kurt() function is quite simple:

DataFrame.kurt(axis=0, skipna=True, level=None, numeric_only=None, **kwargs)

• axis: Specifies the axis along which the kurtosis is calculated. By default, it is 0, meaning the kurtosis is calculated for each column.
• skipna: A boolean value indicating whether to exclude NA/null values. The default is True.
• level: If the input is a multi-index DataFrame, you can specify the level for which you want to calculate the kurtosis.
• numeric_only: A boolean value to include only numeric data types. The default is None, which means all columns are considered.
• **kwargs: Additional keyword arguments.

Parameters of kurt() Function

1. axis: As mentioned earlier, this parameter determines whether you want to calculate the kurtosis column-wise (axis=0) or row-wise (axis=1).
2. skipna: This parameter specifies whether to exclude NA/null values. If set to True, NA/null values are excluded from the calculation, and if set to False, they are treated as zero.
3. level: If your DataFrame has a multi-index, you can use this parameter to specify the level for which you want to calculate the kurtosis.
4. numeric_only: When set to True, only numeric data types are considered for kurtosis calculation. If set to False, all data types are included. If set to None, the function considers all columns.

Interpreting Kurtosis Values

Before we dive into examples, it’s important to understand how to interpret kurtosis values:

• A kurtosis value close to 0 indicates that the distribution has similar tails and peak as a normal distribution.
• Positive kurtosis (greater than 0) indicates heavier tails and a sharper peak compared to a normal distribution. This is often referred to as “leptokurtic.”
• Negative kurtosis (less than 0) suggests lighter tails and a flatter peak compared to a normal distribution. This is often referred to as “platykurtic.”

Examples of Using kurt() Function

Example 1: Analyzing Kurtosis of a Gaussian Distribution

Let’s start with a simple example using a Gaussian distribution, also known as a normal distribution. We’ll generate random data using NumPy and then calculate the kurtosis using Pandas.

import numpy as np
import pandas as pd

# Generate random data from a normal distribution
np.random.seed(42)
data = np.random.normal(0, 1, 1000)

# Create a DataFrame from the data
df = pd.DataFrame(data, columns=['Value'])

# Calculate the kurtosis
kurtosis_value = df['Value'].kurt()

print("Kurtosis:", kurtosis_value)

In this example, since we generated data from a normal distribution, we expect the kurtosis value to be close to 0.

Example 2: Analyzing Kurtosis of a Real-World Dataset

Now, let’s work with a real-world dataset to analyze the kurtosis of a different distribution. We will use the famous Iris dataset, which is available in the Seaborn library. We’ll calculate the kurtosis of the sepal lengths of different iris species.

import seaborn as sns
import pandas as pd

# Load the Iris dataset
iris = sns.load_dataset('iris')

# Calculate the kurtosis of sepal lengths for each species
kurtosis_values = iris.groupby('species')['sepal_length'].apply(pd.Series.kurt)

print("Kurtosis values for sepal lengths:\n")
print(kurtosis_values)

In this example, we calculate the kurtosis values for the sepal lengths of three different species of iris. By examining these values, we can gain insights into how the distributions of sepal lengths vary among the species.

Conclusion

The kurt() function in Pandas is a valuable tool for assessing the shape of distributions in a dataset. By calculating kurtosis, you can quickly identify whether a distribution has heavy or light tails and a sharp or flat peak compared to a normal distribution. This tutorial provided an in-depth overview of the kurt() function, its parameters, and how to interpret its results. You also learned how to apply the function to both synthetic and real-world datasets through practical examples. With this knowledge, you can confidently use the kurt() function to analyze and understand the distributions in your data.