MATLAB Code Implementation for Poisson Distribution Simulation

Poisson distribution simulation in MATLAB can be implemented using built-in functions or custom algorithms. The core objective is to generate random event counts that follow Poisson processes and validate their statistical properties. Implementation Approach Parameter Configuration The Poisson distribution is determined by the event rate parameter λ (lambda). Users need to specify the λ value and the number of simulations (e.g., generating 10,000 samples). Random Number Generation MATLAB's `poissrnd()` function directly generates Poisson random numbers. For manual implementation, leverage the relationship between Poisson processes and exponential distribution: Generate event intervals using `exprnd()` function, and record event counts when cumulative time reaches a threshold. Validation Methods Theoretical Comparison: Calculate sample mean/variance - both should approximate λ in Poisson distribution. Histogram Fitting: Use `histogram()` to display sample distribution, overlaying theoretical curves plotted with `poisspdf()`. Chi-square Test: Quantitatively verify the congruence between sample distribution and theoretical distribution. Extended Applications Can simulate scenarios like telephone call arrivals or network packet arrivals. Observe distribution shape changes by adjusting λ (e.g., distribution approaches normal when λ increases). This simulation is suitable for probability education or communication system modeling, balancing efficiency and accuracy. Key Code Implementation Details: - Use `poissrnd(lambda, m, n)` to generate m×n matrix of Poisson random numbers - Custom algorithm: `cumsum(exprnd(1/lambda, 1, max_events))` for event timeline - Validation code: `mean(samples)`, `var(samples)` for statistical checks - Plotting: `histogram(data, 'Normalization', 'pdf')` with `poisspdf(0:max_count, lambda)` overlay