Pareto {VGAM}R Documentation

The Pareto Distribution


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.

See Also

pareto1, ParetoIV.


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

[Package VGAM version 0.7-7 Index]