Tikuv: 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, lower.tail = TRUE, log.p = FALSE)
qtikuv(p, d, mean = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE, ...)
rtikuv(n, d, mean = 0, sigma = 1, Smallno = 1.0e-6)

Arguments

x, q

vector of quantiles.

vector of probabilities.

number of observations. Same as in runif.

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 lowe

...

Arguments that can be passed into uniroot.

log

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

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

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

Details

See tikuv for more details.

Examples

Run this code

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