probability distributions in R

Overview

Type	Distribution	R Suffix	Comments
Continuous	Normal	-norm()
	Lognormal	-lnorm()	Normally distributed in a log scale
	Uniform	-unif()
Discrete	Binomial	-binom()
	Multinomial	-multinom()	Similar to binomial but when there are more than 2 outcomes
	Poisson	-pois()

Prefix:

• PDF or PMF (d-) e.g. dnorm(x)
• CDF (p-) e.g. pnorm(x)
• the quantile function (q-)
• The random deviate function (-r)

Normal Distribution

• dnorm(x, mean = 0, sd = 1): PDF
• pnorm(x, mean = 0, sd = 1, lower.tail = TRUE) CDF
• qnorm(x, mean = 0, sd = 1, lower.tail = TRUE): quantile function
• rnorm(x, mean = 0, sd = 1): generates random deviates

Explanation

pnorm is the CDF, which is the area under the normal curve below certain threshold. If we set lower.tail = FALSE, we are essentially compute the area above q (a.k.a. 1 - pnorm(x, mean, sd))

qnorm(p, mean = 0, sd = 1, lower.tail = TRUE) calculates the value such that the area of the curve below this value is equal to p.

For example, given a random variable , , pnorm finds , given and qnorm finds given .

Binomial Distribution

See: Binomial

• x: number of events
• n: number of trails
• p or prob: probability of success

The R function family provided by the binomial distribution shares the similar postfixes as the normal distribution.

• dbinom(x, n, p): PMF
• pbinom(x, n, p, lower.tail = TRUE): CDF
• qninom(x, n, p, lower.tail = TRUE): quantile function
• rbinom(x, n, p): generates random deviates

Examples

Compute for

sum(dbinom(46:54, 100, 0.5))

Alternatively

pbinom(54, 100, 0.5) - pbinom(45, 100, 0.5)