TwoParExponential: The 2-Parameter Exponential Distribution

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

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)

Value

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

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 $P [X \leq x]$ , 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 $f (x) = \frac{1}{β} e^{(x - μ) / β}$ where $x \geq μ$ , $μ$ is the shift parameter, and $β > 0$ is the scale parameter.

Examples

Run this code

## 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)

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