Huber {marg} | R Documentation |
Huber's Least Favourable Distribution
Description
Density, cumulative distribution, quantiles and random number generator for Huber's least favourable distribution.
Usage
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 ( |
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. |
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, NA
s 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
pHuber(0.5)
## 0.680374
pHuber(0.5, k = 1.5)
## 0.6842623