Implementing Poisson Process in MATLAB with Parameter Estimation

In this article, we explore how to implement Poisson processes using MATLAB and perform parameter estimation with this powerful computational tool. We begin by introducing the fundamental concepts and definitions of Poisson processes, along with their significance in practical applications such as queuing systems, telecommunications, and risk modeling. The MATLAB implementation section demonstrates how to generate Poisson processes using the exponential distribution for inter-arrival times, leveraging built-in functions like exprnd() for random number generation and cumsum() for event time accumulation. For parameter estimation, we detail the maximum likelihood estimation (MLE) approach using MATLAB's optimization toolbox, specifically the fmincon() function for lambda parameter optimization. The analysis section covers result interpretation through statistical tests including chi-square goodness-of-fit tests and confidence interval calculations using poissfit(). Practical case studies illustrate the application of Poisson processes in real-world scenarios, complete with MATLAB code snippets showing how to validate model assumptions and assess estimation accuracy through residual analysis and Q-Q plots. Readers will gain comprehensive skills in applying Poisson process simulation and parameter estimation techniques in MATLAB, along with understanding their practical implementation value across various domains.