Chernoff {modeest} | R Documentation |
Density, distribution function, quantile function and random generation for the Chernoff distribution.
dchern(x, log = FALSE) pchern(q, lower.tail = TRUE, log.p = FALSE) qchern(p, lower.tail = TRUE, log.p = FALSE) rchern(n)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. |
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]. |
The Chernoff distribution is the law of the random variable
Z = argmax_t (B(t) - t^2)
where B(t) is two-sided Brownian motion starting from zero.
Up to a location and a scale parameter, this distribution is the limit
distribution of the Chernoff mode estimator (also called the naive
mode estimator), see Chernoff (1964).
dchern
gives the density, pchern
gives the distribution
function, qchern
gives the quantile function and rchern
generates random deviates.
Presently, pchern
, qchern
, and rchern
are *very* slow.
Groeneboom and Wellner for the original C code,
Paul Poncet paulponcet@yahoo.fr for the R translation.
dchern
, pchern
and qchern
are calculated
from the C code due to Groeneboom and Wellner (2001).
mlv
for general mode estimation;
naive
for the Chernoff mode estimate;
distribMode
for computation of the mode of the classical distributions
dchern(seq(0.1,0.9,0.1)) curve(dchern(x), xlim = c(-2,2))