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, log=FALSE)
    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, log=FALSE)
    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, log=FALSE)
    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.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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 0.7-9 Index]