# Exponential {stats}

### Description

Density, distribution function, quantile function and random generation for the exponential distribution with rate `rate`

(i.e., mean `1/rate`

).

### Usage

dexp(x, rate = 1, log = FALSE) pexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE) qexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE) rexp(n, rate = 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. - rate
- vector of rates.
- 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 `rate`

is not specified, it assumes the default value of `1`

.

The exponential distribution with rate λ has density f(x) = λ {e}^{- λ x} for x ≥ 0.

### Values

`dexp`

gives the density, `pexp`

gives the distribution function, `qexp`

gives the quantile function, and `rexp`

generates random deviates.

The length of the result is determined by `n`

for `rexp`

, and is the maximum of the lengths of the numerical parameters for the other functions. The numerical parameters other than `n`

are recycled to the length of the result. Only the first elements of the logical parameters are used.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) *The New S Language*. Wadsworth & Brooks/Cole.

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) *Continuous Univariate Distributions*, volume 1, chapter 19. Wiley, New York.

### See Also

`exp`

for the exponential function.

Distributions for other standard distributions, including `dgamma`

for the gamma distribution and `dweibull`

for the Weibull distribution, both of which generalize the exponential.

### Examples

Documentation reproduced from R 3.0.2. License: GPL-2.