Density, cumulative distribution, quantiles and random number generator for Huber's least favourable distribution.
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x |
vector of quantiles. Missing values ( |
q |
vector of quantiles. Missing values ( |
p |
vector of probabilities. Missing values ( |
n |
sample size. If |
k |
tuning constant. Values should preferably lie between 1 and 1.5. The default is 1.345, which gives 95% efficiency at the Normal. |
Inversion of the cumulative distribution function is used to generate deviates from Huber's least favourable distribution.
Density (dHuber
), probability (pHuber
),
quantile (qHuber
), or random sample (rHuber
)
for Huber's least favourable distribution with tuning constant
k
. If values are missing, NA
s will be returned.
The function rHuber
causes creation of the dataset
.Random.seed
if it does not already exist; otherwise its
value is updated.
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.
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.
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