Random Variables with Up to 50 Probability Distributions

Our tool enables the generation of random variables following up to 50 distinct probability distributions, including Nakagami, Rayleigh, and Poisson distributions. These distributions are implemented using robust statistical algorithms - for instance, Nakagami variates are typically generated through transformation methods involving Gamma distributions, while Rayleigh variables can be derived from square root transformations of exponential distributions. Poisson random numbers are commonly implemented via efficient algorithms like the Knuth method or inversion techniques. The applications span multiple domains: in communication systems, Nakagami distribution models multipath fading channel amplitudes; Rayleigh distribution characterizes scattering channel amplitudes; and Poisson distribution describes random event occurrences. Our implementation includes parameter validation and seed management for reproducible results. This tool provides researchers and engineers in communications, signal processing, and statistics with extensive options for simulations and experiments, featuring API functions like generate_nakagami() and get_distribution_parameters() for seamless integration into technical workflows.