ParetoIV {VGAM}R Documentation

The Pareto(IV/III/II) Distributions

Description

Density, distribution function, quantile function and random generation for the Pareto(IV/III/II) distributions.

Usage

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)

Arguments

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.

Details

For the formulas and other details see paretoIV.

Value

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.

Note

The functions [dpqr]paretoI are the same as [dpqr]pareto1 except for a slight change in notation: s=k and b=alpha; see Pareto.

Author(s)

T. W. Yee

References

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.

See Also

paretoIV, Pareto.

Examples

## 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)

[Package VGAM version 0.7-7 Index]