QLMDe {QuantileGH}

Quantile Least Mahalanobis Distance estimates

Description

The quantile least Mahalanobis distance algorithm estimates the parameters of single-component or finite mixture distributions by minimizing the Mahalanobis distance between the vectors of sample and theoretical quantiles. See QLMDp for the default selection of probabilities at which the sample and theoretical quantiles are compared.

The default initial values are estimated based on trimmed k-means clustering with re-assignment.

Usage

QLMDe(
  x,
  distname = c("GH", "norm", "sn"),
  K,
  data.name = deparse1(substitute(x)),
  constraint = character(),
  probs = QLMDp(x = x),
  init = c("logLik", "letterValue", "normix"),
  tol = .Machine$double.eps^0.25,
  maxiter = 1000,
  ...
)

Arguments

x

numeric vector, the one-dimensional observations.

distname

character scalar, name of mixture distribution to be fitted. Currently supports 'norm' and 'GH'.

K

integer scalar, number of components (e.g., must use 2L instead of 2).

data.name

character scalar, name for the observations for user-friendly print out.

constraint

character vector, parameters (g and/or h for Tukey g-&-h mixture) to be set at 0. See function fmx_constraint for details.

probs

numeric vector, percentiles at where the sample and theoretical quantiles are to be matched. See function QLMDp for details.

init

character scalar for the method of initial values selection, or an fmx object of the initial values. See function fmx_hybrid for more details.

tol, maxiter

see function vuniroot2

...

additional parameters of optim

Details

Quantile Least Mahalanobis Distance estimator fits a single-component or finite mixture distribution by minimizing the Mahalanobis distance between the theoretical and observed quantiles, using the empirical quantile variance-covariance matrix quantile_vcov.

Value

Function QLMDe returns an fmx object.

See Also

fmx_hybrid

Examples

data(bmi, package = 'mixsmsn')
hist(x <- bmi[[1L]])
QLMDe(x, distname = 'GH', K = 2L)