| Exponential {stats} | R Documentation |
The Exponential Distribution
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 |
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
|
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.
Note
The cumulative hazard H(t) = - \log(1 - F(t))
is -pexp(t, r, lower = FALSE, log = TRUE).
Source
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.
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,
dgamma for the gamma distribution and
dweibull for the Weibull distribution, both of which
generalize the exponential.
Examples
dexp(1) - exp(-1) #-> 0