Tpareto {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

    dtpareto(x, lower, upper, shape)
    ptpareto(q, lower, upper, shape)
    qtpareto(p, lower, upper, shape)
    rtpareto(n, lower, upper, shape)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a single positive integer.
`lower, upper, shape` | the lower, upper and shape (k) parameters. If necessary, values are recycled.

### Details

See `tpareto1`, 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

`dtpareto` gives the density, `ptpareto` gives the distribution function, `qtpareto` gives the quantile function, and `rtpareto` generates random deviates.

### Author(s)

T. W. Yee

### 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

`tpareto1`.

### Examples

    lower = 3; upper = 8; k = exp(0.5)
    ## Not run:
    x = seq(lower, upper, len=200)
    plot(x, dtpareto(x, lo=lower, up=upper, shape=k), type="l",
         main="Truncated Pareto density split into 10 equal areas")
    abline(h=0, col="blue", lty=2)
    qq = qtpareto(seq(0.1,0.9,by=0.1),lo=lower, up=upper,shape=k)
    lines(qq, dtpareto(qq, lo=lower, up=upper, shape=k),
          col="purple", lty=3, type="h")
    ## End(Not run)
    pp = seq(0.1,0.9,by=0.1)
    qq = qtpareto(pp, lo=lower, up=upper, shape=k)
    ptpareto(qq, lo=lower, up=upper, shape=k)
    qtpareto(ptpareto(qq, lo=lower, up=upper, shape=k),
             lo=lower, up=upper, shape=k) - qq # Should be all 0

[Package VGAM version 0.7-9 Index]