VGAMdata (version 1.1-12)

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)

Value

dtikuv gives the density,

ptikuv gives the cumulative distribution function,

qtikuv gives the quantile function, and

rtikuv generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

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 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.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Author

T. W. Yee and Kai Huang

Details

See tikuv for more details.

See Also

tikuv.

Examples

if (FALSE)  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