mixnorm: Normal Mixture Density
In RBesT: R Bayesian Evidence Synthesis Tools

Description Usage Arguments Details Value Functions See Also Examples

The normal mixture density and auxiliary functions.

mixnorm(..., sigma, param = c("ms", "mn"))

mn2norm(m, n, sigma, drop = TRUE)

## S3 method for class 'normMix'
summary(object, probs = c(0.025, 0.5, 0.975), ...)

## S3 method for class 'normMix'
sigma(object, ...)

sigma(object) <- value

`...`	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`.

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=σ/√{n} with σ being the fixed reference scale.

The reference scale σ 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.

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

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

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

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)