VGAM: huberUC – R documentation

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huberUC

Huber's Least Favourable Distribution

Description

Density, distribution function, quantile function and random generation for Huber's least favourable distribution, see Huber and Ronchetti (2009).

Usage

dhuber(x, k = 0.862, mu = 0, sigma = 1, log = FALSE)
edhuber(x, k = 0.862, mu = 0, sigma = 1, log = FALSE)
 rhuber(n, k = 0.862, mu = 0, sigma = 1)
 qhuber(p, k = 0.862, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
 phuber(q, k = 0.862, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

`x, q`	numeric vector, vector of quantiles.
`p`	vector of probabilities.
`n`	number of random values to be generated. If `length(n) > 1` then the length is taken to be the number required.
`k`	numeric. Borderline value of central Gaussian part of the distribution. This is known as the tuning constant, and should be positive. For example, `k = 0.862` refers to a 20% contamination neighborhood of the Gaussian distribution. If `k = 1.40` then this is 5% contamination.
`mu`	numeric. distribution mean.
`sigma`	numeric. Distribution scale (`sigma = 1` defines the distribution in standard form, with standard Gaussian centre).
`log`	Logical. If `log = TRUE` then the logarithm of the result is returned.
`lower.tail, log.p`	Same meaning as in `pnorm` or `qnorm`.

Details

Details are given in huber2, the VGAM family function for estimating the parameters mu and sigma.

Value

dhuber gives out a vector of density values.

edhuber gives out a list with components val (density values) and eps (contamination proportion).

rhuber gives out a vector of random numbers generated by Huber's least favourable distribution.

phuber gives the distribution function, qhuber gives the quantile function.

Author(s)

Christian Hennig wrote [d,ed,r]huber() (from smoothmest) and slight modifications were made by T. W. Yee to replace looping by vectorization and addition of the log argument. Arash Ardalan wrote [pq]huber(), and two arguments for these were implemented by Kai Huang. This helpfile was adapted from smoothmest.

Examples

set.seed(123456)
edhuber(1:5, k = 1.5)
rhuber(5)

## Not run:  mu <- 3; xx <- seq(-2, 7, len = 100)  # Plot CDF and PDF
plot(xx, dhuber(xx, mu = mu), type = "l", col = "blue", las = 1, ylab = "",
     main = "blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles",
     ylim = 0:1)
abline(h = 0, col = "blue", lty = 2)
lines(xx, phuber(xx, mu = mu), type = "l", col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qhuber(probs, mu = mu)
lines(Q, dhuber(Q, mu = mu), col = "purple", lty = 3, type = "h")
lines(Q, phuber(Q, mu = mu), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
phuber(Q, mu = mu) - probs  # Should be all 0s

## End(Not run)

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