R: Huber's least favourable distribution

dhuber {smoothmest} | R Documentation

## Huber's least favourable distribution

### Description

Density for and random values from Huber's least favourable distribution, see Huber and Ronchetti (2009).

### Usage

      dhuber(x, k=0.862, mu=0, sigma=1)
      edhuber(x, k=0.862, mu=0, sigma=1)
      rhuber(n,k=0.862, mu=0, sigma=1)

### Arguments

`x` | numeric vector.
`k` | numeric. Borderline value of central Gaussian part of the distribution. The default values refers to a 20% contamination neighborhood of the Gaussian distribution.
`mu` | numeric. distribution mean.
`sigma` | numeric. Distribution scale (`sigma=1` defines the distribution in standard form, with standard Gaussian centre).
`n` | integer. Number of random values to be generated.

### Details

dhuber:

  density.

edhuber:

  density, and computes the contamination proportion corresponding to `k`.

rhuber:

  random number generation.

### 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.

### Author(s)

Christian Hennig chrish@stats.ucl.ac.uk http://www.homepages.ucl.ac.uk/~ucakche/

### References

Huber, P. J. and Ronchetti, E. (2009) Robust Statistics (2nd ed.). Wiley, New York.

### Examples

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

[Package smoothmest version 0.1-2 Index]