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
print(x, ...)
# 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.
x: The mixture to print
object: Normal mixture object.
probs: Quantiles reported by the summary function.
value: New value of the reference scale sigma.

Functions

sigma(object) <- value: 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 $s = σ / \sqrt{n}$ 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.

Examples

Run this code


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

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

set.seed(57845)
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)

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