"Huber density" distribution
Density, distribution function, quantile function and random generation for the "Huber density" distribution.
dhuber(x, mu = 0, sigma = 1, epsilon = 1.345, log = FALSE) phuber(q, mu = 0, sigma = 1, epsilon = 1.345, lower.tail = TRUE, log.p = FALSE) qhuber(p, mu = 0, sigma = 1, epsilon = 1.345, lower.tail = TRUE, log.p = FALSE) rhuber(n, mu = 0, sigma = 1, epsilon = 1.345)
x, q |
vector of quantiles. |
mu, sigma, epsilon |
location, and scale, and shape parameters. Scale and shape must be positive. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. |
p |
vector of probabilities. |
n |
number of observations. If |
Huber density is connected to Huber loss and can be defined as:
f(x) = 1/(2 * sqrt(2π) * (Φ(k) + φ(k)/k - 1/2)) * exp(-ρ(x, k))
where
ρ(x, k) = [if abs(x) <= k:] (x^2)/2 [else:] k*abs(x) - (k^2)/2
Huber, P.J. (1964). Robust Estimation of a Location Parameter. Annals of Statistics, 53(1), 73-101.
Huber, P.J. (1981). Robust Statistics. Wiley.
Schumann, D. (2009). Robust Variable Selection. ProQuest.
x <- rhuber(1e5, 5, 2, 3) hist(x, 100, freq = FALSE) curve(dhuber(x, 5, 2, 3), -20, 20, col = "red", add = TRUE, n = 5000) hist(phuber(x, 5, 2, 3)) plot(ecdf(x)) curve(phuber(x, 5, 2, 3), -20, 20, col = "red", lwd = 2, add = TRUE)
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