Huber's Least Favourable Distribution

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Description

Density, cumulative distribution, quantiles and random number generator for Huber's least favourable distribution.

Usage

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dHuber(x, k = 1.345)
pHuber(q, k = 1.345)
qHuber(p, k = 1.345)
rHuber(n, k = 1.345)

Arguments

x

vector of quantiles. Missing values (NAs) are allowed.

q

vector of quantiles. Missing values (NAs) are allowed.

p

vector of probabilities. Missing values (NAs) are allowed.

n

sample size. If length(n) is larger than 1, then length(n) random values are returned.

k

tuning constant. Values should preferably lie between 1 and 1.5. The default is 1.345, which gives 95% efficiency at the Normal.

Details

Inversion of the cumulative distribution function is used to generate deviates from Huber's least favourable distribution.

Value

Density (dHuber), probability (pHuber), quantile (qHuber), or random sample (rHuber) for Huber's least favourable distribution with tuning constant k. If values are missing, NAs will be returned.

Side Effects

The function rHuber causes creation of the dataset .Random.seed if it does not already exist; otherwise its value is updated.

Background

Huber's least favourable distribution is a compound distribution with gaussian behaviour in the interval (-k,k) and double exponential tails. It is strongly related to Huber's M-estimator, which represents the maximum likelihood estimator of the location parameter.

References

Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986) Robust Statistics: The Approach Based on Influence Functions. New York: Wiley.

Examples

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pHuber(0.5)
## 0.680374
pHuber(0.5, k = 1.5)
## 0.6842623

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