Exponential {stats}R Documentation

The Exponential Distribution


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.
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].


If rate is not specified, it assumes the default value of 1.

The exponential distribution with rate λ has density

f(x) = lambda e^(- lambda x)

for x >= 0.


dexp gives the density, pexp gives the distribution function, qexp gives the quantile function, and rexp generates random deviates.


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


dexp, pexp and qexp are all calculated from numerically stable versions of the definitions.

rexp uses

Ahrens, J. H. and Dieter, U. (1972). Computer methods for sampling from the exponential and normal distributions. Communications of the ACM, 15, 873–882.


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, dgamma for the gamma distribution and dweibull for the Weibull distribution, both of which generalize the exponential.


dexp(1) - exp(-1) #-> 0

[Package stats version 2.9.0 Index]