ParetoIV {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation for the Pareto(IV/III/II) distributions.
dparetoIV(x, location=0, scale=1, inequality=1, shape=1) pparetoIV(q, location=0, scale=1, inequality=1, shape=1) qparetoIV(p, location=0, scale=1, inequality=1, shape=1) rparetoIV(n, location=0, scale=1, inequality=1, shape=1) dparetoIII(x, location=0, scale=1, inequality=1) pparetoIII(q, location=0, scale=1, inequality=1) qparetoIII(p, location=0, scale=1, inequality=1) rparetoIII(n, location=0, scale=1, inequality=1) dparetoII(x, location=0, scale=1, shape=1) pparetoII(q, location=0, scale=1, shape=1) qparetoII(p, location=0, scale=1, shape=1) rparetoII(n, location=0, scale=1, shape=1) dparetoI(x, scale=1, shape=1) pparetoI(q, scale=1, shape=1) qparetoI(p, scale=1, shape=1) rparetoI(n, scale=1, shape=1)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. Must be a single positive integer. |
location |
the location parameter. |
scale, shape, inequality |
the (positive) scale, inequality and shape parameters. |
For the formulas and other details
see paretoIV
.
Functions beginning with the letter d
give the density,
functions beginning with the letter p
give the distribution function,
functions beginning with the letter q
give the quantile function, and
functions beginning with the letter r
generates random deviates.
The functions [dpqr]paretoI
are the same as [dpqr]pareto1
except for a slight change in notation: s=k and
b=alpha; see Pareto
.
T. W. Yee
Brazauskas, V. (2003) Information matrix for Pareto(IV), Burr, and related distributions. Comm. Statist. Theory and Methods 32, 315–325.
Arnold, B. C. (1983) Pareto Distributions. Fairland, Maryland: International Cooperative Publishing House.
## Not run: x = seq(-0.2, 4, by=0.01) loc = 0; Scale = 1; ineq = 1; shape = 1.0; plot(x, dparetoIV(x, loc, Scale, ineq, shape), type="l", col="blue", main="Blue is density, red is cumulative distribution function", sub="Purple are 5,10,...,95 percentiles", ylim=0:1, las=1, ylab="") abline(h=0, col="blue", lty=2) Q = qparetoIV(seq(0.05,0.95,by=0.05), loc, Scale, ineq, shape) lines(Q, dparetoIV(Q, loc, Scale, ineq, shape), col="purple", lty=3, type="h") lines(x, pparetoIV(x, loc, Scale, ineq, shape), col="red") abline(h=0, lty=2) ## End(Not run)