Uniform                package: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 <= 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) = 1/(max-min)

     for min <= x <= max.

     For the case of u := min == max, the limit case of X == 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

