A Short-tailed Symmetric Distribution
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, 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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as in |
d, mean, sigma |
arguments for the parameters of the distribution.
See |
Smallno |
Numeric, a small value used by the rejection method for determining
the lower and upper limits of the distribution.
That is, |
... |
Arguments that can be passed into |
log |
Logical.
If |
lower.tail, log.p |
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 and Kai Huang
## 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)))
## End(Not run)
probs <- seq(0.1, 0.9, by = 0.1)
ptikuv(qtikuv(p = probs, d = 1), d = 1) - probs # Should be all 0Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.