Exponential {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 *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)`

.

### 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

[Package

*stats* version 2.9.0

Index]