# PDF of Sum of Independent Exponential Random Variables

Version 1.0 (6.54 KB) by
This code package contains a helper function sumexppdf() designed to generate PDF/CDF of sum of independent exponential RVs.
Updated 22 Nov 2023

# sumexppdf.m MATLAB Helper Function

This code package contains a helper function `sumexppdf()` designed to generate Probability Density Functions (PDF) and Cumulative Distribution Functions (CDF) for the sum of independent exponential random variables.

Functionality:

The function computes the PDF of the sum of independent exponential random variables: Y = X_1 + X_2 + X_3 + ... + X_n.

When provided with weights as the third input argument, it computes the PDF of the weighted sum of independent exponential random variables: Y = a_1.X_1 + a_2.X_2 + ... + a_n.X_n

Note: Only positive weights are supported.

Author: Zakir Hussain Shaik Contact: zakir.b2a@gmail.com

Function Inputs:

• `t` (Mandatory): Value at which PDF/CDF is evaluated
• `lambdas` (Mandatory): Parameters of Exponential Random Variables
• `weights` (Optional): Weights of Random Variables

Function Outputs:

• `f`: PDF evaluated at `t`
• `F`: CDF evaluated at `t`

Usage Examples:

```f = sumexppdf(t, lambdas); % or [f, F] = sumexppdf(t, lambdas);
f = sumexppdf(t, lambdas, weights); % or [f, F] = sumexppdf(t, lambdas, weights);```

Function Details:

Function Version: 1.0 License: This code is licensed under the GPLv2 license. Compatibility: MATLAB (tested on 2023a) Additional Information: This file is accompanied by example scripts and an illustration on obtaining the PDF of the norm square of a complex Gaussian vector.

For theoretical expressions and further discussions, refer to the accompanying blog article: https://www.zakirtechblog.com/post/sumexppdf/

### Cite As

Zakir Hussain (2024). PDF of Sum of Independent Exponential Random Variables (https://github.com/zakirhussainshaik/sumexppdf_matlab/releases/tag/v1.0), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2023b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux