Distributions in R

One of the R language's most powerful features is its ability to deal with random distributions: not just generating random numbers from various distributions (based on a very powerful pseudo-random number generator), but also calculating densities, probabilities, and quintiles. John Cook provides a handy reference chart listing all of the distributions supported by standard R (reproduced below -- and there are many other distributions supported by contributed packages), and also explains the elegant naming scheme for the various functions.

Distribution	Base name	Parameters
beta	beta	shape1, shape2, ncp
binomial	binom	size, prob
Cauchy	cauchy	location, scale
chi-squared	chisq	df, ncp
exponential	exp	rate
F	f	df1, df2, ncp
gamma	gamma	shape, rate
geometric	geom	p
hypergeometric	hyper	m, n, k
log-normal	lnorm	meanlog, sdlog
logistic	logis	location, scale
negative binomial	nbinom	size, prob
normal	norm	mean, sd
Poisson	pois	lambda
Student t	t	df, ncp
uniform	unif	min, max
Weibull	weibull	shape, scale

Updated Aug 20: added the ncp parameter to beta, chisq, f, and t with thanks to Doug Bates' comment below.

John D Cook: Distributions in R and S-PLUS

Comments

[Douglas Bates]

The argument lists in this table for the beta, chisq, f and t distributions are incomplete. R allows for a non-centrality parameter, ncp, in each of these distributions. (If I recall correctly, S-PLUS does not but I don't have a copy of that software available to check.)

Allowing for non-central versions of these distributions in R took a considerable amount of work, especially by Martin Maechler, and I think it should be acknowledged.

[David Smith]

Thanks for pointing that out Doug, I updated the post above. Martin and others from the R project definitely deserve a round of applause -- the accuracy of these functions, especially in the tails, is unparalleled. I didn't include some of the other parameters like lower.tail which give even more accuracy in some situations -- follow the links in the table to read up on the other options.