PDF of Sum of Independent Exponential Random Variables

This code package contains a helper function sumexppdf() designed to generate PDF/CDF of sum of independent exponential RVs.

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: [e-mail]

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/