WenJun Zhang School of Life Sciences, Sun Yat-sen University, Guangzhou 510275, China Selforganizology ISSN 2410-0080 http://www.iaees.org/publications/journals/selforganizology/online-version.asp 2026 13 3-4 26 65 International Academy of Ecology and Environmental Sciences Hong Kong 8 August 2025 26 September 2025 1 December 2026 calculator web application JavaScript probability distribution binomial distribution Poisson distribution exponential distribution gamma distribution beta distribution uniform distribution Weibull distribution lognormal distribution Cauchy distribution geometric distribution negative binomial distribution In this study, I developed probFunCal2, an advanced web-based calculator for probability distribution functions that complements the original probFunCal by providing comprehensive support for additional probability distributions. The calculator includes binomial, Poisson, exponential, gamma, beta, uniform, Weibull, lognormal, Cauchy, geometric, and negative binomial distributions. For each distribution, probFunCal2 calculates probability density/mass functions (PDF/PMF), cumulative distribution functions (CDF), and inverse cumulative distribution functions (quantiles). The implementation uses sophisticated numerical methods including Stirling's approximation for factorials, continued fraction methods for regularized incomplete beta and gamma functions, and various quantile approximations. The calculator is fully browser-based, supporting both online and offline usage across multiple platforms and devices. This tool provides researchers, students, and practitioners with a robust, accessible platform for statistical computations essential for probability theory, statistical inference, and data analysis. http://www.iaees.org/publications/journals/selforganizology/articles/2026-13(3-4)/probFunCal2-for-advanced-probability-distribution-functions.pdf