R: The Uniform Distribution

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 ≤ 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.

### 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.

### Note

The characteristics of output from pseudo-random number generators (such as precision and periodicity) vary widely. See `.Random.seed` for more information on R's random number generation algorithms.

### 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

[Package stats version 4.0.5 Index]