# 2ParExponential: The 2-Parameter Exponential Distribution In tolerance: Statistical Tolerance Intervals and Regions

## Description

Density, distribution function, quantile function, and random generation for the 2-parameter exponential distribution with rate equal to `rate` and shift equal to `shift`.

## Usage

 ```1 2 3 4``` ```d2exp(x, rate = 1, shift = 0, log = FALSE) p2exp(q, rate = 1, shift = 0, lower.tail = TRUE, log.p = FALSE) q2exp(p, rate = 1, shift = 0, lower.tail = TRUE, log.p = FALSE) r2exp(n, rate = 1, shift = 0) ```

## Arguments

 `x,q` Vector of quantiles. `p` Vector of probabilities. `n` The number of observations. If `length>1`, then the length is taken to be the number required. `rate` Vector of rates. `shift` Vector of shifts. `log,log.p` Logical vectors. If `TRUE`, then probabilities are given as `log(p)`. `lower.tail` Logical vector. If `TRUE`, then probabilities are P[X≤ x], else P[X>x].

## Details

If `rate` or `shift` are not specified, then they assume the default values of 1 and 0, respectively.

The 2-parameter exponential distribution has density

f(x) = exp(-(x-μ)/β)/β,

where x≥μ, μ is the shift parameter, and β>0 is the scale parameter.

## Value

`d2exp` gives the density, `p2exp` gives the distribution function, `q2exp` gives the quantile function, and `r2exp` generates random deviates.

`runif` and `.Random.seed` about random number generation.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## Randomly generated data from the 2-parameter exponential ## distribution. set.seed(100) x <- r2exp(n = 500, rate = 3, shift = -10) hist(x, main = "Randomly Generated Data", prob = TRUE) x.1 = sort(x) y <- d2exp(x = x.1, rate = 3, shift = -10) lines(x.1, y, col = 2, lwd = 2) plot(x.1, p2exp(q = x.1, rate = 3, shift = -10), type = "l", xlab = "x", ylab = "Cumulative Probabilities") q2exp(p = 0.20, rate = 3, shift = -10, lower.tail = FALSE) q2exp(p = 0.80, rate = 3, shift = -10) ```

### Example output  ```Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE