Statistical Intervals, 2nd Edition

Appendix C Useful Probability Distributions

Introduction

This appendix provides notation, expressions for the density or the probability mass function (pmf), the cumulative distribution function, the quantiles, the mean, and the variance for distributions that are important in setting different kinds of statistical intervals. Most of the presentation is descriptive, but when needed we provide some technical details.

The topics discussed in this appendix are:

• The relationship between the symbols used in our formulas in this book and the arguments used by the R software package (R Core Team, 2016) for the pdf/pmf, cdf, and quantile functions (Section C.1).
• Information about important functions related to the probability distributions used in this book, namely the cdf, pdf, and quantile functions (Section C.2).
• Continuous distributions used in the book (Section C.3).
• Discrete distributions used in the book (Section C.4).

C.1 Probability Distributions and R Computations

In some places in this book, we show how to do simple computations where the software package R is used as a sophisticated calculator that can not only perform the usual scientific hand calculator functions (e.g., add, subtract, multiply, divide, log, antilog, and square root), but also compute probabilities and quantiles of particular distributions used in constructing confidence intervals (replacing tables that were utilized before the advent of personal computers). To aid readers who are new to R, Table C.1 ...