Exponential              package: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 lambda 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)'.

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, 'dgamma' for the gamma
     distribution and 'dweibull' for the Weibull distribution, both of
     which generalize the exponential.

Examples:

     dexp(1) - exp(-1) #-> 0

