
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)
vector of quantiles.
vector of probabilities.
number of observations.
Same as in runif
.
arguments for the parameters of the distribution.
See tikuv
for more details.
For rtikuv
, arguments mean
and sigma
must be of
length 1.
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
.
Logical.
If log = TRUE
then the logarithm of the density is returned.
dtikuv
gives the density,
ptikuv
gives the cumulative distribution function,
qtikuv
gives the quantile function, and
rtikuv
generates random deviates.
See tikuv
for more details.
# 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)))
# }
# NOT RUN {
probs <- seq(0.1, 0.9, by = 0.1)
ptikuv(qtikuv(p = probs, d = 1), d = 1) - probs # Should be all 0
# }
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