# Uniform

##### The Uniform Distribution

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.

- Keywords
- distribution

##### 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.

##### 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

`library(stats)`

```
# NOT RUN {
u <- runif(20)
## The following relations always hold :
punif(u) == u
dunif(u) == 1
var(runif(10000)) #- ~ = 1/12 = .08333
# }
```

*Documentation reproduced from package stats, version 3.6.2, License: Part of R 3.6.2*

### Community examples

**richie@datacamp.com**at Jan 17, 2017 stats v3.3.1

Generate 20 random numbers from a uniform distribution between 0 and 1. ```{r} runif(20) ``` As above, but with a uniform distribution from -5 to 5. ```{r} runif(20, -5, 5) ``` The probability density function (PDF), cumulative density function (CDF), and inverse CDF. ```{r} lo <- -5 hi <- 5 x <- seq(lo - 1, hi + 1, 0.01) pdf_of_x <- dunif(x, lo, hi) cdf_of_x <- punif(x, lo, hi) probabilities <- seq(0, 1, 0.01) inverse_cdf_of_x <- qunif(probabilities, lo, hi) layout(matrix(1:3)) plot(x, pdf_of_x, type = "l", main = "PDF of x") plot(x, cdf_of_x, type = "l", main = "CDF of x") plot(probabilities, inverse_cdf_of_x, type = "l", , main = "Inverse CDF of x") ``` If you want log probabilities, the `log`/`log.p` argument is faster than calling the log function afterwards ```{r} lo <- -5 hi <- 5 x <- seq(lo - 1, hi + 1, 0.01) microbenchmark::microbenchmark( log(punif(x, lo, hi)), punif(x, lo, hi, log.p = TRUE) # same but faster ) ```