nor1mix (version 1.0-7)

pnorMix: Normal Mixture Cumulative Distribution and Quantiles

Description

Compute cumulative probabilities or quantiles (the inverse) for a normal mixture specified as norMix object.

Usage

pnorMix(q, obj, lower.tail = TRUE, log.p = FALSE)
qnorMix(p, obj, lower.tail = TRUE, log.p = FALSE,
        tol = .Machine$double.eps^0.25, maxiter = 1000)

Arguments

obj

an object of class norMix.

p

numeric vector of probabilities.

q

numeric vector of quantiles

lower.tail

logical; if TRUE (default), probabilities are $P[X \le x]$, otherwise, $P[X > x]$.

log.p

logical; if TRUE, probabilities p are given as log(p).

tol, maxiter

determine the root finding algorithm, see uniroot.

Value

• a numeric vector of the same length as p or q, respectively.

encoding

latin1

Details

Whereas the distribution function pnorMix is the trivial sum of weighted normal probabilities (pnorm), its inverse is currently computed numerically using uniroot to find q such that pnorMix(obj, q) == p.

See Also

dnorMix for the density function.

Examples

MW.nm3 # the "strange skew" one
plot(MW.nm3)
## now the cumlative :
x <- seq(-4,4, length=1001)
plot(x, pnorMix(x, MW.nm3), type="l", col=2)
## and some of its inverse :
pp <- seq(.1, .9, by=.1)
plot(qnorMix(pp, MW.nm3), pp)

## The "true" median of a normal mixture:
median.norMix <- function(x) qnorMix(1/2, x)
median.norMix(MW.nm3) ## -2.32