| Pareto {VGAM} | R Documentation |
Density, distribution function, quantile function and random
generation for the Pareto(I) distribution with parameters
location and shape.
dpareto(x, location, shape) ppareto(q, location, shape) qpareto(p, location, shape) rpareto(n, location, shape)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. Must be a single positive integer. |
location, shape |
the alpha and k parameters. |
See pareto1, 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.
dpareto gives the density,
ppareto gives the distribution function,
qpareto gives the quantile function, and
rpareto generates random deviates.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
alpha = 3; k = exp(1); x = seq(2.8, 8, len=300)
## Not run:
plot(x, dpareto(x, location=alpha, shape=k), type="l",
main="Pareto density split into 10 equal areas")
abline(h=0, col="blue", lty=2)
qq = qpareto(seq(0.1,0.9,by=0.1),location=alpha,shape=k)
lines(qq, dpareto(qq, loc=alpha, shape=k), col="purple", lty=3, type="h")
## End(Not run)
pp = seq(0.1,0.9,by=0.1)
qq = qpareto(pp, location=alpha, shape=k)
ppareto(qq, location=alpha, shape=k)
qpareto(ppareto(qq,loc=alpha,shape=k),loc=alpha,shape=k) - qq # Should be 0