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.
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)
.
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.
Distributions for other standard distributions, including
dgamma
for the gamma distribution and
dweibull
for the Weibull distribution, both of which
generalize the exponential.
Examples
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))