Chernoff {modeest}R Documentation

The Chernoff Distribution

Description

Density, distribution function, quantile function and random generation for the Chernoff distribution.

Usage

dchern(x, log = FALSE)
pchern(q, lower.tail = TRUE, log.p = FALSE)
qchern(p, lower.tail = TRUE, log.p = FALSE)
rchern(n)

Arguments

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].

Details

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).

Value

dchern gives the density, pchern gives the distribution function, qchern gives the quantile function and rchern generates random deviates.

Warning

Presently, pchern, qchern, and rchern are *very* slow.

Author(s)

Groeneboom and Wellner for the original C code,
Paul Poncet paulponcet@yahoo.fr for the R translation.

Source

dchern, pchern and qchern are calculated from the C code due to Groeneboom and Wellner (2001).

References

See Also

mlv for general mode estimation; naive for the Chernoff mode estimate; distribMode for computation of the mode of the classical distributions

Examples

dchern(seq(0.1,0.9,0.1))
curve(dchern(x), xlim = c(-2,2))

[Package modeest version 1.06 Index]