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 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 <= x], otherwise, P[X > x].

Details

If rate is not specified, it assumes the default value of 1.

The exponential distribution with rate λ has density

f(x) = lambda e^(- lambda x)

for x >= 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).

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

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
[Package Contents]