Package {QuantileGH}

Type:	Package
Title:	Quantile Least Mahalanobis Distance Estimator for Tukey g-&-h Mixture
Version:	0.3.0
Date:	2026-07-16
Description:	Functions for simulation, estimation, and model selection of finite mixtures of Tukey g-and-h distributions. The author has retired from academic research. Accordingly, this package should not be considered a validated tool for use in peer-reviewed publications or as the basis for grant applications. Backward compatibility with user-code published in <doi:10.1007/s11222-025-10596-9> is not maintained in versions >= 0.3.0 (July 2026) of this package. The authors of those publications are the appropriate contacts for reproducibility inquiries.
License:	GPL-2
Encoding:	UTF-8
Language:	en-US
Depends:	R (≥ 4.6)
Imports:	cli
Config/roxygen2/version:	8.0.0
NeedsCompilation:	no
Packaged:	2026-07-16 14:07:53 UTC; tingtingzhan
Author:	Tingting Zhan [aut, cre]
Maintainer:	Tingting Zhan <tingtingzhan@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-16 20:50:07 UTC

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

Description

Functions for simulation, estimation, and model selection of finite mixtures of Tukey g-and-h distributions. The author has retired from academic research. Accordingly, this package should not be considered a validated tool for use in peer-reviewed publications or as the basis for grant applications. Backward compatibility with user-code published in doi:10.1007/s11222-025-10596-9 is not maintained in versions >= 0.3.0 (July 2026) of this package. The authors of those publications are the appropriate contacts for reproducibility inquiries.

Details

Tools for simulating and fitting finite mixtures of the 4-parameter Tukey g-&-h distributions. Tukey g-&-h mixture is highly flexible to model multimodal distributions with variable degree of skewness and kurtosis in the components. The Quantile Least Mahalanobis Distance estimator (QLMDe) is used for estimating parameters of the finite Tukey g-&-h mixtures. QLMDe is an indirect estimator that minimizes the Mahalanobis distance between the sample and model-based quantiles. A backward-forward stepwise model selection algorithm is provided to find

• a parsimonious Tukey g-&-h mixture model, conditional on a given number-of-components; and

• the optimal number of components within the user-specified range.

Note

This R package author has retired from academic research.

Accordingly, this package should not be considered a validated tool for use in peer-reviewed publications or as the basis for grant applications.

Backward compatibility with user-code published in the following publications is not maintained in versions ⁠>= 0.3.0⁠ of this package. The authors of those publications are the appropriate contacts for reproducibility inquiries.

doi:10.1007/s11222-025-10596-9

Author(s)

Maintainer: Tingting Zhan tingtingzhan@gmail.com (ORCID)

Authors:

• Tingting Zhan tingtingzhan@gmail.com (ORCID)

Determine Nearly-Equal Elements

Description

Determine nearly-equal elements and extract non-nearly-equal elements in a double vector.

Usage

unique_allequal(x, ...)

duplicated_allequal(x, ...)

Arguments

Value

Function duplicated_allequal() returns a logical vector of the same length as the input vector, indicating whether each element is nearly-equal to any of the previous elements.

Function unique_allequal() returns the non-nearly-equal elements in the input vector.

See Also

duplicated.default unique.default

Examples

(x = c(.3, 1-.7, 0, .Machine$double.eps))
duplicated.default(x) # not desired
unique.default(x) # not desired
duplicated_allequal(x)
unique_allequal(x)
unique_allequal(x, tol = .Machine$double.eps/2)

Test if Two double Vectors are Element-Wise (Nearly) Equal

Description

Test if two double vectors are element-wise (nearly) equal.

Usage

allequal_o_(target, current, tolerance = sqrt(.Machine$double.eps), ...)

Arguments

Details

Function allequal_o_() is different from all.equal.numeric, such that

• only compares between double, not complex, values

• element-wise comparison is performed, in a fashion similar to function outer

• a logical scalar is always returned for each element-wise comparison.

Value

Function allequal_o_() returns an n_t\times n_c logical matrix indicating whether the length-n_c vector current is element-wise near-equal to the length-n_t vector target within the pre-specified tolerance.

Examples

allequal_o_(target = c(.3, 0), current = c(.3, 1-.7, 0, .Machine$double.eps))

Simpler and Faster Mahalanobis Distance

Description

Simpler and faster mahalanobis distance.

Usage

mahalanobis_(x, center, invcov)

Arguments

Value

Function mahalanobis_() returns a numeric scalar.

Examples

# ?stats:::mahalanobis
S = cbind(1:6, 1:3) |> var()
mahalanobis(c(0, 0), 1:2, S)
mahalanobis_(c(0, 0), 1:2, solve(S))