The Inverse Exponential Distribution — invexp • invgamma

Density, distribution function, quantile function and random generation for the inverse exponential distribution.

Usage

dinvexp(x, rate = 1, log = FALSE)

pinvexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)

qinvexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE)

rinvexp(n, rate = 1)

Arguments

x, q: vector of quantiles.
rate: degrees of freedom (non-negative, but can be non-integer).
log, log.p: logical; if TRUE, probabilities p are given as log(p).
lower.tail: logical; if TRUE (default), probabilities are \(P[X \leq x]\); if FALSE \(P[X > x]\).
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The functions (d/p/q/r)invexp() simply wrap those of the standard (d/p/q/r)exp() R implementation, so look at, say, stats::dexp() for details.

See also

stats::dexp(); these functions just wrap the (d/p/q/r)exp() functions.

Examples


s <- seq(0, 10, .01)
plot(s, dinvexp(s, 2), type = 'l')


f <- function(x) dinvexp(x, 2)
q <- 3
integrate(f, 0, q)
#> 0.5134171 with absolute error < 6.7e-06
(p <- pinvexp(q, 2))
#> [1] 0.5134171
qinvexp(p, 2) # = q
#> [1] 3
mean(rinvexp(1e5, 2) <= q)
#> [1] 0.51292

pinvgamma(q, 1, 2)
#> [1] 0.5134171