Tpareto {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation
for the upper truncated Pareto(I) distribution with parameters
lower
, upper
and shape
.
dtpareto(x, lower, upper, shape) ptpareto(q, lower, upper, shape) qtpareto(p, lower, upper, shape) rtpareto(n, lower, upper, shape)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. Must be a single positive integer. |
lower, upper, shape |
the lower, upper and shape (k) parameters. If necessary, values are recycled. |
See tpareto1
, the VGAM family function
for estimating the parameter k by maximum likelihood estimation,
for the formula of the probability density function and the
range restrictions imposed on the parameters.
dtpareto
gives the density,
ptpareto
gives the distribution function,
qtpareto
gives the quantile function, and
rtpareto
generates random deviates.
T. W. Yee
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.
lower = 3; upper = 8; k = exp(0.5) ## Not run: x = seq(lower, upper, len=200) plot(x, dtpareto(x, lo=lower, up=upper, shape=k), type="l", main="Truncated Pareto density split into 10 equal areas") abline(h=0, col="blue", lty=2) qq = qtpareto(seq(0.1,0.9,by=0.1),lo=lower, up=upper,shape=k) lines(qq, dtpareto(qq, lo=lower, up=upper, shape=k), col="purple", lty=3, type="h") ## End(Not run) pp = seq(0.1,0.9,by=0.1) qq = qtpareto(pp, lo=lower, up=upper, shape=k) ptpareto(qq, lo=lower, up=upper, shape=k) qtpareto(ptpareto(qq, lo=lower, up=upper, shape=k), lo=lower, up=upper, shape=k) - qq # Should be all 0