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
$X == u$ 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)
u <- runif(20)
## The following relations always hold :
punif(u) == u
dunif(u) == 1
var(runif(10000)) #- ~ = 1/12 = .08333
Community examples
--- title: "Introduction to Data Frames in R" output: html_notebook --- ```{r } runif(200) ```
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 ) ```