R Cookbook

Chapter 8. Probability

Introduction

Probability theory is the foundation of statistics, and R has plenty of machinery for working with probability, probability distributions, and random variables. The recipes in this chapter show you how to calculate probabilities from quantiles, calculate quantiles from probabilities, generate random variables drawn from distributions, plot distributions, and so forth.

Names of Distributions

R has an abbreviated name for every probability distribution. This name is used to identify the functions associated with the distribution. For example, the name of the Normal distribution is “norm”, which is the root of these function names:

Function	Purpose
dnorm	Normal density
pnorm	Normal distribution function
qnorm	Normal quantile function
rnorm	Normal random variates

Table 8-1 describes some common discrete distributions, and Table 8-2 describes several common continuous distributions.

Table 8-1. Discrete distributions

Discrete distribution	R name	Parameters
Binomial	binom	n = number of trials; p = probability of success for one trial
Geometric	geom	p = probability of success for one trial
Hypergeometric	hyper	m = number of white balls in urn; n = number of black balls in urn; k = number of balls drawn from urn
Negative binomial (NegBinomial)	nbinom	size = number of successful trials; either prob = probability of successful trial or mu = mean
Poisson	pois	lambda = mean

Table 8-2. Continuous distributions

Continuous distribution	R name	Parameters
Beta	beta	shape1; shape2
Cauchy	cauchy	location; ...