R: The Truncated Pareto Distribution

Truncpareto {VGAM} | R Documentation

## The Truncated Pareto Distribution

### Description

Density, distribution function, quantile function and random generation for the upper truncated Pareto(I) distribution with parameters `lower`, `upper` and `shape`.

### Usage

    dtruncpareto(x, lower, upper, shape, log = FALSE)
    ptruncpareto(q, lower, upper, shape, lower.tail = TRUE, log.p = FALSE)
    qtruncpareto(p, lower, upper, shape)
    rtruncpareto(n, lower, upper, shape)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n, log` | Same meaning as `runif`.
`lower, upper, shape` | the lower, upper and shape (k) parameters. If necessary, values are recycled.
`lower.tail, log.p` | Same meaning as in `pnorm` or `qnorm`.

### Details

See `truncpareto`, 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.

### Value

`dtruncpareto` gives the density, `ptruncpareto` gives the distribution function, `qtruncpareto` gives the quantile function, and `rtruncpareto` generates random deviates.

### Author(s)

T. W. Yee and Kai Huang

### References

Aban, I. B., Meerschaert, M. M. and Panorska, A. K. (2006) Parameter estimation for the truncated Pareto distribution, Journal of the American Statistical Association, 101(473), 270–277.

### See Also

`truncpareto`.

### Examples

     lower <- 3; upper <- 8; kay <- exp(0.5)
    ## Not run:  xx <- seq(lower - 0.5, upper + 0.5, len = 401)
    plot(xx, dtruncpareto(xx, low = lower, upp = upper, shape = kay),
         main = "Truncated Pareto density split into 10 equal areas",
         type = "l", ylim = 0:1, xlab = "x")
    abline(h = 0, col = "blue", lty = 2)
    qq <- qtruncpareto(seq(0.1, 0.9, by = 0.1), low = lower, upp = upper,
                       shape = kay)
    lines(qq, dtruncpareto(qq, low = lower, upp = upper, shape = kay),
          col = "purple", lty = 3, type = "h")
    lines(xx, ptruncpareto(xx, low = lower, upp = upper, shape = kay),
          col = "orange")
    ## End(Not run)
    pp <- seq(0.1, 0.9, by = 0.1)
    qq <- qtruncpareto(pp, lower = lower, upper = upper, shape = kay)

    ptruncpareto(qq, lower = lower, upper = upper, shape = kay)
    qtruncpareto(ptruncpareto(qq, lower = lower, upper = upper, shape = kay),
             lower = lower, upper = upper, shape = kay) - qq  # Should be all 0

[Package VGAM version 1.0-3 Index]