| Exponential {stats} | R Documentation |
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 |
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) = 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 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.
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.
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))