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Exponential {stats}

The Exponential Distribution
R 3.0.2


Density, distribution function, quantile function and random generation for the exponential distribution with rate rate (i.e., mean 1/rate).


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)


x, q
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length is taken to be the number required.
vector of rates.
log, log.p
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].


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.


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.


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.


The cumulative hazard H(t) = - log(1 - F(t)) is -pexp(t, r, lower = FALSE, log = TRUE).

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.


dexp(1) - exp(-1) #-> 0
## a fast way to generate *sorted*  U[0,1]  random numbers:
rsunif <- function(n) { n1 <- n+1
   cE <- cumsum(rexp(n1)); cE[seq_len(n)]/cE[n1] }
plot(rsunif(1000), ylim=0:1, pch=".")
abline(0,1/(1000+1), col=adjustcolor(1, 0.5))

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