- 1 - Compendium of Distributions, I: Beta, Binomial, Chi-Square, F, Gamma, Geometric, Poisson, Student's t, and Uniform. Maurice HT Ling School of Chemical and Life Sciences, Singapore Polytechnic, Singapore Department of Zoology, The University of Melbourne, Australia mauriceling@acm.org Abstract This manuscript illustrates the implementation and testing of nine statistical distributions, namely Beta, Binomial, Chi-Square, F, Gamma, Geometric, Poisson, Student’s t and Uniform distribution, where each distribution consists of three common functions – Probability Density Function (PDF), Cumulative Density Function (CDF) and the inverse of CDF (inverseCDF). 1. Description Statistical distributions play a central role in statistical inferences to provide a probabilistic measure for use in hypothesis testing. As such, the implementation of statistical distributions and functions is fundamental to high-throughput scientific analyses. This manuscript illustrates the implementation of nine statistical distributions (McLaughlin, 2001); namely Beta, Binomial, Chi-Square, F, Gamma, Geometric, Poisson, Student’s t and Uniform; where each distribution consists of three common functions – Probability Density Function (PDF), Cumulative Density Function (CDF) and the inverse of CDF (inverseCDF) – as modelled after Ling (2009). Of these nine distributions presented in this manuscript, two are discrete distributions (Binomial and Poisson) whereas the rest are continuous distributions (Beta, Chi-Square, F, Gamma, Geometric, Student’s t and Uniform). Each distribution can be briefly described as follows: • Beta distribution is a continuous distribution bounded between zero and one. This constraint rendered its use to model the probability of event occurrences (Keefer et al., 1993) or approximating the value of variables (Haskett et al., 1995). • Binomial distribution is a discrete distribution commonly used to model the outcomes of a series of experiments with only two possible outcomes per experiment (Van der Geest, 2005). • Chi-Square distribution is a continuous distribution commonly used to measure the association between two categorical variables (Ugoni and Walker, 1995). • F distribution (Crofts, 1982) is a joint distribution of two independent variables, each having a Chi-Square distribution. Gamma distribution (Jambunathan, 1954) is related to Chi-Square distribution and had been used in likelihood estimation (Rogers, 2001).