VGAM: ParetoUC – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

ParetoUC

The Pareto Distribution

Description

Density, distribution function, quantile function and random generation for the Pareto(I) distribution with parameters scale and shape.

Usage

dpareto(x, scale = 1, shape, log = FALSE)
ppareto(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
qpareto(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE)
rpareto(n, scale = 1, shape)

Arguments

`x, q`	vector of quantiles.
`p`	vector of probabilities.
`n`	number of observations. Same as in `runif`.
`scale, shape`	the alpha and k 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

See paretoff, 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

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and rpareto generates random deviates.

Author(s)

T. W. Yee and Kai Huang

References

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

Examples

alpha <- 3; k <- exp(1); x <- seq(2.8, 8, len = 300)
## Not run: 
plot(x, dpareto(x, scale = alpha, shape = k), type = "l",
     main = "Pareto density split into 10 equal areas")
abline(h = 0, col = "blue", lty = 2)
qvec <- qpareto(seq(0.1, 0.9, by = 0.1), scale = alpha, shape = k)
lines(qvec, dpareto(qvec, scale = alpha, shape = k),
      col = "purple", lty = 3, type = "h")

## End(Not run)
pvec <- seq(0.1, 0.9, by = 0.1)
qvec <- qpareto(pvec, scale = alpha, shape = k)
ppareto(qvec, scale = alpha, shape = k)
qpareto(ppareto(qvec, scale = alpha, shape = k),
        scale = alpha, shape = k) - qvec  # Should be 0

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13