| Tikuv {VGAM} | R Documentation |
Density, cumulative distribution function, quantile function and random generation for the short-tailed symmetric distribution of Tiku and Vaughan (1999).
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)
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.
|
See tikuv for more details.
dtikuv gives the density,
ptikuv gives the cumulative distribution function,
qtikuv gives the quantile function, and
rtikuv generates random deviates.
T. W. Yee
## Not run:
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
## End(Not run)