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 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 \le x], otherwise, P[X > x].

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)

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