R: The Pareto(IV/III/II) Distributions

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,
              lower.tail = TRUE, log.p = FALSE)
    qparetoIV(p, location = 0, scale = 1, inequality = 1, shape = 1,
              lower.tail = TRUE, log.p = FALSE)
    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,
               lower.tail = TRUE, log.p = FALSE)
    qparetoIII(p, location = 0, scale = 1, inequality = 1,
               lower.tail = TRUE, log.p = FALSE)
    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,
              lower.tail = TRUE, log.p = FALSE)
    qparetoII(p, location = 0, scale = 1, shape = 1,
              lower.tail = TRUE, log.p = FALSE)
    rparetoII(n, location = 0, scale = 1, shape = 1)
    dparetoI(x, scale = 1, shape = 1, log = FALSE)
    pparetoI(q, scale = 1, shape = 1,
             lower.tail = TRUE, log.p = FALSE)
    qparetoI(p, scale = 1, shape = 1,
             lower.tail = TRUE, log.p = FALSE)
    rparetoI(n, scale = 1, shape = 1)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Same as in `runif`.
`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.
`lower.tail, log.p` | Same meaning as in `pnorm` or `qnorm`.

### 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]pareto` except for a slight change in notation: s=k and b=alpha; see `Pareto`.

### Author(s)

T. W. Yee and Kai Huang

### 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, orange 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 = "orange")
    abline(h = 0, lty = 2)

    ## End(Not run)

[Package VGAM version 1.1-3 Index]