stats (version 3.4.1)

Uniform: The Uniform Distribution

Description

These functions provide information about the uniform distribution on the interval from min to max. dunif gives the density, punif gives the distribution function qunif gives the quantile function and runif generates random deviates.

Usage

dunif(x, min = 0, max = 1, log = FALSE)
punif(q, min = 0, max = 1, lower.tail = TRUE, log.p = FALSE)
qunif(p, min = 0, max = 1, lower.tail = TRUE, log.p = FALSE)
runif(n, min = 0, max = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

min, max

lower and upper limits of the distribution. Must be finite.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

Value

dunif gives the density, punif gives the distribution function, qunif gives the quantile function, and runif generates random deviates. The length of the result is determined by n for runif, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

Details

If min or max are not specified they assume the default values of 0 and 1 respectively.

The uniform distribution has density $$f(x) = \frac{1}{max-min}$$ for \(min \le x \le max\).

For the case of \(u := min == max\), the limit case of \(X \equiv u\) is assumed, although there is no density in that case and dunif will return NaN (the error condition).

runif will not generate either of the extreme values unless max = min or max-min is small compared to min, and in particular not for the default arguments.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

See Also

RNG about random number generation in R.

Distributions for other standard distributions.

Examples

u <- runif(20)

## The following relations always hold :
punif(u) == u
dunif(u) == 1

var(runif(10000))  #- ~ = 1/12 = .08333