# Exponential: The Exponential Distribution In Rlab: Functions and Datasets Required for ST370 class

## 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

 ```1 2 3 4``` ```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 <= x], otherwise, P[X > x].

## Details

If `beta` (or `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)`.

## References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth \& Brooks/Cole.

`exp` for the exponential function, `dgamma` for the gamma distribution and `dweibull` for the Weibull distribution, both of which generalize the exponential.

## Examples

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

### Example output

```Rlab 2.15.1 attached.

Attaching package: 'Rlab'

The following objects are masked from 'package:stats':

dexp, dgamma, dweibull, pexp, pgamma, pweibull, qexp, qgamma,
qweibull, rexp, rgamma, rweibull

The following object is masked from 'package:datasets':

precip

[1] 0
```

Rlab documentation built on May 30, 2017, 3:26 a.m.