Exponential
The Exponential Distribution
Density, distribution function, quantile function and random
generation for the exponential distribution with rate rate
(i.e., mean 1/rate).
- Keywords
- distribution
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 \(P[X \le x]\), otherwise, \(P[X > x]\).
Details
If rate is not specified, it assumes the default value of
1.
The exponential distribution with rate \(\lambda\) has density $$f(x) = \lambda {e}^{- \lambda x}$$ for \(x \ge 0\).
Value
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 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 cumulative hazard \(H(t) = - \log(1 - F(t))\)
is -pexp(t, r, lower = FALSE, log = TRUE).
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
library(stats)
# NOT RUN {
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))
# }