R: The Exponential Distribution

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 <= x], otherwise, P[X > x].

### Details

If `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)`.

### 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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