Perks: The Perks Distribution

Description

Density, cumulative distribution function, quantile function and random generation for the Perks distribution.

Usage

dperks(x, scale = 1, shape, log = FALSE)
pperks(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
qperks(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
rperks(n, scale = 1, shape)

Arguments

x, q

vector of quantiles.

vector of probabilities.

number of observations. Same as in runif.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

shape, scale

positive shape and scale parameters.

Value

dperks gives the density, pperks gives the cumulative distribution function, qperks gives the quantile function, and rperks generates random deviates.

Details

See perks for details.

Examples

Run this code

probs <- seq(0.01, 0.99, by = 0.01)
Shape <- exp(-1.0); Scale <- exp(1);
max(abs(pperks(qperks(p = probs, Shape, Scale),
                  Shape, Scale) - probs))  # Should be 0

x <- seq(-0.1, 07, by = 0.01);
plot(x, dperks(x, Shape, Scale), type = "l", col = "blue", las = 1,
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles",
     ylab = "", ylim = 0:1)
abline(h = 0, col = "blue", lty = 2)
lines(x, pperks(x, Shape, Scale), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qperks(probs, Shape, Scale)
lines(Q, dperks(Q, Shape, Scale), col = "purple", lty = 3, type = "h")
pperks(Q, Shape, Scale) - probs  # Should be all zero
abline(h = probs, col = "purple", lty = 3)

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