R: A Short-tailed Symmetric Distribution

Tikuv {VGAM}

R Documentation

A Short-tailed Symmetric Distribution

Description

Density, cumulative distribution function, quantile function and random generation for the short-tailed symmetric distribution of Tiku and Vaughan (1999).

Usage

dtikuv(x, d, mean = 0, sigma = 1, log = FALSE)
ptikuv(q, d, mean = 0, sigma = 1)
qtikuv(p, d, mean = 0, sigma = 1, ...)
rtikuv(n, d, mean = 0, sigma = 1, Smallno = 1.0e-6)

Arguments

`x, q`	vector of quantiles.
`p`	vector of probabilities.
`n`	number of observations. Must be a positive integer of length 1.
`d, mean, sigma`	arguments for the parameters of the distribution. See `tikuv` for more details. For `rtikuv`, arguments `mean` and `sigma` must be of length 1.
`Smallno`	Numeric, a small value used by the rejection method for determining the lower and upper limits of the distribution. That is, `ptikuv(L) < Smallno` and `ptikuv(U) > 1-Smallno` where `L` and `U` are the lower and upper limits respectively.
`...`	Arguments that can be passed into `uniroot`.
`log`	Logical. If `log = TRUE` then the logarithm of the density is returned.

Details

See tikuv for more details.

Value

dtikuv gives the density, ptikuv gives the cumulative distribution function, qtikuv gives the quantile function, and rtikuv generates random deviates.

Author(s)

T. W. Yee

Examples

## Not run:  par(mfrow = c(2, 1))
x = seq(-5, 5, len = 401)
plot(x, dnorm(x), type = "l", col = "black", ylab = "", las = 1,
     main = "Black is standard normal, others are dtikuv(x, d)")
lines(x, dtikuv(x, d = -10), col = "orange")
lines(x, dtikuv(x, d = -1 ), col = "blue")
lines(x, dtikuv(x, d =  1 ), col = "green")
legend("topleft", col = c("orange","blue","green"), lty = rep(1, len = 3),
       legend = paste("d =", c(-10, -1, 1)))

plot(x, pnorm(x), type = "l", col = "black", ylab = "", las = 1,
     main = "Black is standard normal, others are ptikuv(x, d)")
lines(x, ptikuv(x, d = -10), col = "orange")
lines(x, ptikuv(x, d = -1 ), col = "blue")
lines(x, ptikuv(x, d =  1 ), col = "green")
legend("topleft", col = c("orange","blue","green"), lty = rep(1, len = 3),
       legend = paste("d =", c(-10, -1, 1)))

probs = seq(0.1, 0.9, by = 0.1)
ptikuv(qtikuv(p = probs, d =  1), d = 1) - probs  # Should be all 0

## End(Not run)

[Package VGAM version 0.8-4 Index]