Bayesian Psychometric Modeling

Appendix B: Probability Distributions

This appendix presents and briefly discusses features of some standard probability distributions, as an aid to understanding their use throughout the book. In each case, we present the notation, probability mass or density function, and summary quantities such as the mean, variance, and mode (where applicable). In addition, we discuss common usage of these distributions. We use the notation x for a random variable and x for a random vector, except in the cases of the Wishart and inverse-Wishart where we use W and W⁻¹ to stand for the random matrix, respectively. For deeper discussions of these and other distributions, see Casella and Berger (2008), Gelman et al. (2013), and Jackman (2009). See Lunn et al. ...