Uniform {stats}

R Documentation

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].

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

.Random.seed about random number generation, rnorm, etc for other distributions.

Examples

u <- runif(20)

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

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

---