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Density, distribution function, quantile function and random
generation for the upper truncated Pareto(I) distribution with
parameters lower
, upper
and shape
.
dtruncpareto(x, lower, upper, shape, log = FALSE)
ptruncpareto(q, lower, upper, shape, lower.tail = TRUE, log.p = FALSE)
qtruncpareto(p, lower, upper, shape)
rtruncpareto(n, lower, upper, shape)
dtruncpareto
gives the density,
ptruncpareto
gives the distribution function,
qtruncpareto
gives the quantile function, and
rtruncpareto
generates random deviates.
T. W. Yee and Kai Huang
See truncpareto
, the VGAM family function
for estimating the parameter
Aban, I. B., Meerschaert, M. M. and Panorska, A. K. (2006). Parameter estimation for the truncated Pareto distribution, Journal of the American Statistical Association, 101(473), 270--277.
truncpareto
.
lower <- 3; upper <- 8; kay <- exp(0.5)
if (FALSE) xx <- seq(lower - 0.5, upper + 0.5, len = 401)
plot(xx, dtruncpareto(xx, low = lower, upp = upper, shape = kay),
main = "Truncated Pareto density split into 10 equal areas",
type = "l", ylim = 0:1, xlab = "x")
abline(h = 0, col = "blue", lty = 2)
qq <- qtruncpareto(seq(0.1, 0.9, by = 0.1), low = lower, upp = upper,
shape = kay)
lines(qq, dtruncpareto(qq, low = lower, upp = upper, shape = kay),
col = "purple", lty = 3, type = "h")
lines(xx, ptruncpareto(xx, low = lower, upp = upper, shape = kay),
col = "orange")
pp <- seq(0.1, 0.9, by = 0.1)
qq <- qtruncpareto(pp, lower = lower, upper = upper, shape = kay)
ptruncpareto(qq, lower = lower, upper = upper, shape = kay)
qtruncpareto(ptruncpareto(qq, lower = lower, upper = upper, shape = kay),
lower = lower, upper = upper, shape = kay) - qq # Should be all 0
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