VGAM (version 0.9-1)

Perks: The Perks Distribution

Description

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

Usage

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

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

log

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

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.

See Also

perks.

Examples

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)