Rlab (version 1.1)

Exponential: 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 $P[X \le x]$, otherwise, $P[X > x]$.

Value

• dexp gives the density, pexp gives the distribution function, qexp gives the quantile function, and rexp generates random deviates.

Details

If beta (or 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 $x \ge 0$.

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