Help for package denstest

Title:

Density Equality Testing

Version:

1.0.0

Description:

Methods for testing the equality between groups of estimated density functions. The package implements FDET (Fourier-based Density Equality Testing) and MDET (Moment-based Density Equality Testing), two new approaches introduced by the author. Both methods extend an earlier testing approach by Delicado (2007), "Functional k-sample problem when data are density functions" <doi:10.1007/s00180-007-0047-y>, which is referred to as DET (Density Equality Testing) in this package for clarity. FDET compares groups of densities based on their global shape using Fourier transforms, while MDET tests for differences in distributional moments. All methods are described in Anarat, Krutmann and Schwender (2025), "Testing for Differences in Extrinsic Skin Aging Based on Density Functions" (Submitted).

License:

GPL-3

VignetteBuilder:

knitr

Suggests:

knitr, rmarkdown

Encoding:

UTF-8

RoxygenNote:

7.3.2

NeedsCompilation:

Packaged:

2025-05-14 08:49:04 UTC; Akin

Author:

Akin Anarat [aut, cre]

Maintainer:

Akin Anarat <akin.anarat@hhu.de>

Repository:

CRAN

Date/Publication:

2025-05-16 09:50:10 UTC

Computation of Test Statistics for Density Equality Tests

Description

Computes the test statistics used in the denstest package for assessing equality between groups of estimated density functions. It supports all implemented methods (FDET, DET, and MDET), but does not perform permutation-based inference. The function is intended for users who want to inspect, compare, or further process the raw values of the test statistics without calculating p-values.

Usage

compute_B(
  L,
  group_sizes,
  N.max = 10000,
  a = NULL,
  b = NULL,
  m = 100,
  seed = NULL,
  density.weights = NULL,
  test = c("FDET.regular", "FDET.residual", "FDET.regular.real.imag",
    "FDET.residual.real.imag", "DET.regular", "DET.residual", "MDET.regular",
    "MDET.residual"),
  distance = c("LP", "Hellinger", "TF"),
  moment = c("expectation", "variance", "skewness", "kurtosis", "combined"),
  interpolation = c("linear", "spline"),
  p = 2,
  eps = 0.01,
  tau = 0.01,
  Lmax = 5000,
  ft.lp.weight = c("none", "AbsRoot"),
  real.imag.weights = c(0.5, 0.5),
  moment.weights = rep(0.25, 4),
  plot = FALSE,
  legend = c("topright", "topleft", "bottomright", "bottomleft", "top", "bottom", "left",
    "right", "center")
)

Arguments

L

A list of estimated density objects, where each element is a list with numeric vectors x and y. x contains the evaluation points, and y the corresponding estimated density values for a single observation.

group_sizes

A vector indicating the number of densities in each group.

N.max

Maximum number of permutations for the test (default: 10000).

a, b

Evaluation range endpoints; if NULL, determined from data.

m

Number of evaluation points (default: 100).

seed

Random seed for reproducibility.

density.weights

Optional weights for densities.

test

The test to use. One of "FDET.regular", "FDET.residual", "FDET.regular.real.imag", "FDET.residual.real.imag", "DET.regular", "DET.residual", "MDET.regular", or "MDET.residual".

distance

The distance measure to use for FDET or DET. One of "LP", "Hellinger", or "TF".

moment

Moment type used for MDET. One of "expectation", "variance", "skewness", "kurtosis", or "combined".

interpolation

Method for interpolating densities. One of "linear" or "spline".

p

Parameter for L^p distances (default: 2).

eps

Cut-off parameter for the Fourier transforms.

tau

Step size parameter of the Fourier Transforms.

Lmax

Maximum size of the vectors containing the values of the individual Fourier transforms.

ft.lp.weight

Weights for the Fourier transforms. One of "none" or "AbsRoot".

real.imag.weights

Weights for the real and imaginary parts of the Fourier transforms.

moment.weights

Internal parameters for specific methods.

plot

Logical. If TRUE, plots the density functions in L.

legend

Position of the legend in the plot.

Value

Test statistic value indicating the degree of separation between groups of estimated density functions.

Author(s)

Akin Anarat akin.anarat@hhu.de

References

Anarat A., Krutmann, J., and Schwender, H. (2025). Testing for Differences in Extrinsic Skin Aging Based on Density Functions. Submitted.

Delicado, P. (2007). Functional k-sample problem when data are density functions. Computational Statistics, 22, 391–410. doi:10.1007/s00180-007-0047-y

Examples

n1 <- 5; n2 <- 5; n3 <- 5
group_sizes <- c(n1, n2, n3)
sample_size <- 500

densities_group1 <- lapply(1:n1, function(i) {
  data <- rnorm(sample_size, 0, 0.3)
  d <- density(data)
  list(x = d$x, y = d$y)
})

densities_group2 <- lapply(1:n2, function(i) {
  data <- rnorm(sample_size, 0, 0.32)
  d <- density(data)
  list(x = d$x, y = d$y)
})

densities_group3 <- lapply(1:n3, function(i) {
  data <- rnorm(sample_size, 0.02, 0.28)
  d <- density(data)
  list(x = d$x, y = d$y)
})

L <- c(densities_group1, densities_group2, densities_group3)

compute_B(L, group_sizes, ft.lp.weight = "AbsRoot")