VGAM (version 0.7-5)

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)
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)

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.

See Also

tikuv.

Examples

x = seq(-5, 5, len=401)
plot(x, dnorm(x), type="l", col="black", ylab="",
     main="Black is standard normal, others are dtikuv(x, d)")
lines(x, dtikuv(x, d=-10), col="red")
lines(x, dtikuv(x, d=-1 ), col="blue")
lines(x, dtikuv(x, d= 1 ), col="green")
legend(2, 0.35, col=c("red","blue","green"), lty=rep(1, len=3),
       legend=paste("d =", c(-10, -1, 1)))

plot(x, pnorm(x), type="l", col="black", ylab="",
     main="Black is standard normal, others are ptikuv(x, d)")
lines(x, ptikuv(x, d=-10), col="red")
lines(x, ptikuv(x, d=-1 ), col="blue")
lines(x, ptikuv(x, d= 1 ), col="green")
legend(2, 0.35, col=c("red","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