| Exponential {base} | 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).
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
r <- rexp(100)
all(abs(1 - dexp(1, r) / (r*exp(-r))) < 1e-14)