The Topp-Leone Distribution
Density, distribution function, quantile function and random generation for the Topp-Leone distribution.
dtopple(x, shape, log = FALSE) ptopple(q, shape, lower.tail = TRUE, log.p = FALSE) qtopple(p, shape) rtopple(n, shape)
See topple, the VGAM family function for
estimating the (shape) parameter s by maximum likelihood
estimation, for the formula of the probability density function.
dtopple gives the density,
ptopple gives the distribution function,
qtopple gives the quantile function, and
rtopple generates random deviates.
The Topp-Leone distribution is related to the triangle distribution.
T. W. Yee
Topp, C. W. and F. C. Leone (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50, 209–219.
## Not run: shape <- 0.7; x <- seq(0.02, 0.999, length = 300)
plot(x, dtopple(x, shape = shape), type = "l", col = "blue", las = 1,
main = "Blue is density, orange is cumulative distribution function",
sub = "Purple lines are the 10,20,...,90 percentiles", ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(x, ptopple(x, shape = shape), type = "l", col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qtopple(probs, shape = shape)
lines(Q, dtopple(Q, shape), col = "purple", lty = 3, type = "h")
lines(Q, ptopple(Q, shape), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(ptopple(Q, shape) - probs)) # Should be zero
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.