RBesT (version 1.6-3)

mixnorm: Normal Mixture Density

Description

The normal mixture density and auxiliary functions.

Usage

mixnorm(..., sigma, param = c("ms", "mn"))
mn2norm(m, n, sigma, drop = TRUE)
# S3 method for normMix
summary(object, probs = c(0.025, 0.5, 0.975), ...)
# S3 method for normMix
sigma(object, ...)
sigma(object) <- value

Value

Returns a normal mixture with the specified mixture components. mn2norm returns the mean and standard deviation given a mean and sample size parametrization.

Arguments

...

list of mixture components.

sigma

reference scale.

param

determines how the parameters in the list are interpreted. See details.

m

vector of means

n

vector of sample sizes.

drop

delete the dimensions of an array which have only one level.

object

normal mixture object.

probs

quantiles reported by the summary function.

value

new value of the reference scale sigma.

Functions

• sigma<-: Allows to assign a new reference scale sigma.

Details

Each entry in the ... argument list is expected to be a triplet of numbers which defines the weight \(w_k\), first and second parameter of the mixture component \(k\). A triplet can optionally be named which will be used appropriately.

The first and second parameter can be given in different parametrizations which is set by the param option:

ms

Mean and standard deviation. Default.

mn

Mean and number of observations. n determines s via the relation \(s=\sigma/\sqrt{n}\) with \(\sigma\) being the fixed reference scale.

The reference scale \(\sigma\) is the fixed standard deviation in the one-parameter normal-normal model (observation standard deviation). The function sigma can be used to query the reference scale and may also be used to assign a new reference scale, see examples below. In case the sigma is not specified, the user has to supply sigma as argument to functions which require a reference scale.

See Also

Other mixdist: mixbeta(), mixcombine(), mixgamma(), mix, plot.mix()

Examples

nm <- mixnorm(rob=c(0.2, 0, 2), inf=c(0.8, 2, 2), sigma=5)

print(nm)
summary(nm)
plot(nm)

set.seed(1)
mixSamp <- rmix(nm, 500)
plot(nm, samp=mixSamp)

# support defined by quantiles
qmix(nm, c(0.01, 0.99))

# density function
dmix(nm, seq(-5,5,by=2))

# distribution function
pmix(nm, seq(-5,5,by=2))

# the reference scale can be changed (it determines the ESS)
ess(nm)

sigma(nm) <- 10
ess(nm)