Exponential Distribution in NumPy Last Updated : 10 Dec, 2025 Comments Improve Suggest changes 1 Likes Like Report The Exponential Distribution is a continuous probability distribution that describes the time between two events in a Poisson process, where events occur independently and at a constant average rate. NumPy provides a simple method to generate such random values: numpy.random.exponential().Example: This example shows how to generate one exponential random value using the default parameters. Python import numpy as np x = np.random.exponential() print(x) Output0.5339358426948082 Explanation: np.random.exponential() generates one value following the exponential distribution.Since no parameters are passed, it uses scale = 1 by default.Syntaxnumpy.random.exponential(scale=1.0, size=None)Parameters:scale: Inverse of the event rate (β = 1/λ).size: Shape of output array.ExamplesExample 1: This example generates one exponential random value using a custom scale. Python import numpy as np x = np.random.exponential(scale=2) print(x) Output0.8177243559186411 Explanation:scale=2 values will be more spread out.x holds a single exponential random number.Larger scale values make the distribution longer and wider.Example 2: This example generates five random numbers from the exponential distribution. Python import numpy as np arr = np.random.exponential(scale=1.5, size=5) print(arr) Output[2.14106221 1.93254045 0.03957526 0.58763751 1.12814399] Explanationscale=1.5 moderate spread.size=5 returns 5 values.arr stores the array like [0.21, 1.33, 0.94, ...].Visualizing the Exponential DistributionVisualizing the generated numbers helps in understanding their behavior. Below is an example of plotting a histogram of random numbers generated using numpy.random.exponential. Python import numpy as np import matplotlib.pyplot as plt import seaborn as sns s = 2 # scale n = 800 # number of points data = np.random.exponential(scale=s, size=n) sns.histplot(data, bins=30, kde=True, edgecolor='black') plt.title(f"Exponential Distribution (Scale={s})") plt.xlabel("Value") plt.ylabel("Frequency") plt.grid(True) plt.show() OutputExponenetial Distribution PlotExplanation:s = 2 sets the spread of the distribution.n = 800 creates enough data points for a smooth histogram.sns.histplot() shows: Bars -> simulated data and Curve (kde) -> smooth theoretical shapeThe graph shows high frequency near 0 and a long decreasing tail, which is typical of exponential distributions. Create Quiz Comment J jitender_1998 Follow 1 Improve J jitender_1998 Follow 1 Improve Article Tags : Python Python-numpy Python numpy-Random Explore Python FundamentalsPython Introduction 2 min read Input and Output in Python 4 min read Python Variables 4 min read Python Operators 4 min read Python Keywords 2 min read Python Data Types 8 min read Conditional Statements in Python 3 min read Loops in Python - For, While and Nested Loops 5 min read Python Functions 5 min read Recursion in Python 4 min read Python Lambda Functions 5 min read Python Data StructuresPython String 5 min read Python Lists 4 min read Python Tuples 4 min read Python Dictionary 3 min read Python Sets 6 min read Python Arrays 7 min read List Comprehension in Python 4 min read Advanced PythonPython OOP Concepts 11 min read Python Exception Handling 5 min read File Handling in Python 4 min read Python Database Tutorial 4 min read Python MongoDB Tutorial 3 min read Python MySQL 9 min read Python Packages 10 min read Python Modules 3 min read Python DSA Libraries 15 min read List of Python GUI Library and Packages 3 min read Data Science with PythonNumPy Tutorial - Python Library 3 min read Pandas Tutorial 4 min read Matplotlib Tutorial 5 min read Python Seaborn Tutorial 3 min read StatsModel Library - Tutorial 3 min read Learning Model Building in Scikit-learn 6 min read TensorFlow Tutorial 2 min read PyTorch Tutorial 6 min read Web Development with PythonFlask Tutorial 8 min read Django Tutorial | Learn Django Framework 7 min read Django ORM - Inserting, Updating & Deleting Data 4 min read Templating With Jinja2 in Flask 6 min read Django Templates 5 min read Build a REST API using Flask - Python 3 min read Building a Simple API with Django REST Framework 3 min read Python PracticePython Quiz 1 min read Python Coding Practice 1 min read Python Interview Questions and Answers 15+ min read Like