Exponential: The Exponential Distribution

In Rlab: Functions and Datasets Required for ST370 Class

The Exponential Distribution

Description

Density, distribution function, quantile function and random generation for the exponential distribution with mean beta or 1/rate).

This special Rlab implementation allows the parameter beta to be used, to match the function description often found in textbooks.

Usage

dexp(x, rate = 1, beta = 1/rate, log = FALSE)
pexp(q, rate = 1, beta = 1/rate, lower.tail = TRUE, log.p = FALSE)
qexp(p, rate = 1, beta = 1/rate, lower.tail = TRUE, log.p = FALSE)
rexp(n, rate = 1, beta = 1/rate)

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.
beta	vector of means.
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 beta (or 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

Rlab documentation built on May 5, 2022, 1:05 a.m.