Triangle {VGAM} | R Documentation |
Density, distribution function, quantile function and random
generation for the Triangle distribution with parameter
theta
.
dtriangle(x, theta, lower = 0, upper = 1, log = FALSE)
ptriangle(q, theta, lower = 0, upper = 1, lower.tail = TRUE, log.p = FALSE)
qtriangle(p, theta, lower = 0, upper = 1, lower.tail = TRUE, log.p = FALSE)
rtriangle(n, theta, lower = 0, upper = 1)
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Same as |
theta |
the theta parameter which lies between |
lower , upper |
lower and upper limits of the distribution. Must be finite. |
log |
Logical.
If |
lower.tail , log.p |
See triangle
,
the VGAM family function
for estimating the parameter \theta
by
maximum likelihood estimation, however the regular
conditions do not hold so the algorithm crawls
to the solution if lucky.
dtriangle
gives the density,
ptriangle
gives the distribution function,
qtriangle
gives the quantile function, and
rtriangle
generates random deviates.
T. W. Yee and Kai Huang
## Not run: x <- seq(-0.1, 1.1, by = 0.01); theta <- 0.75
plot(x, dtriangle(x, theta = theta), type = "l", col = "blue", las = 1,
main = "Blue is density, orange is the CDF",
sub = "Purple lines are the 10,20,...,90 percentiles",
ylim = c(0,2), ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(x, ptriangle(x, theta = theta), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qtriangle(probs, theta = theta)
lines(Q, dtriangle(Q, theta = theta), col = "purple", lty = 3, type = "h")
ptriangle(Q, theta = theta) - probs # Should be all zero
abline(h = probs, col = "purple", lty = 3)
## End(Not run)