truncparetoUC: The Truncated Pareto Distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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

Usage

 ```1 2 3 4``` ```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.

`truncpareto`.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ``` 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 ```

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