fmx_cluster: Naive Estimates of Finite Mixture Distribution via Clustering

In QuantileGH: Quantile Least Mahalanobis Distance Estimator for Tukey g-&-h Mixture

Naive Estimates of Finite Mixture Distribution via Clustering

Description

Naive estimates for finite mixture distribution fmx via clustering.

Usage

fmx_cluster(
  x,
  K,
  distname = c("GH", "norm", "sn"),
  constraint = character(),
  ...
)

Arguments

x	numeric vector, observations
K	integer scalar, number of mixture components
distname	character scalar, name of parametric distribution of the mixture components
constraint	character vector, parameters (g and/or h for Tukey g-&-h mixture) to be set at 0. See function fmx_constraint for details.
...	additional parameters, currently not in use

Details

First of all, if the specified number of components K\geq 2, trimmed k-means clustering with re-assignment will be performed; otherwise, all observations will be considered as one single cluster. The standard k-means clustering is not used since the heavy tails of Tukey g-&-h distribution could be mistakenly classified as individual cluster(s).

In each of the one or more clusters,

• letterValue-based estimates of Tukey g-&-h distribution (Hoaglin, 2006) are calculated, for any K\geq 1, serving as the starting values for QLMD algorithm. These estimates are provided by function fmx_cluster().

• the median and mad will serve as the starting values for \mu and \sigma (or A and B for Tukey g-&-h distribution, with g = h = 0), for QLMD algorithm when K = 1.

Value

Function fmx_cluster() returns an fmx object.

QuantileGH documentation built on April 3, 2025, 8:35 p.m.