| Title: | Self-Similarity Test for Normality |
| Version: | 1.0.1 |
| Description: | Implements the Self-Similarity Test for Normality (SSTN), a new statistical test designed to assess whether a given sample originates from a normal distribution. The method exploits the self-similarity property of the normal characteristic function by iteratively transforming and comparing standardized empirical characteristic functions. The null distribution of the test statistic is obtained via Monte Carlo simulation. Details of the methodology are described in Anarat and Schwender (2026), "A test for normality based on self-similarity", <doi:10.48550/arXiv.2604.03810>. |
| Imports: | MASS |
| License: | GPL-3 |
| VignetteBuilder: | knitr |
| Suggests: | knitr, rmarkdown |
| Encoding: | UTF-8 |
| Language: | en-US |
| RoxygenNote: | 7.3.3 |
| Depends: | R (≥ 3.5) |
| NeedsCompilation: | no |
| Packaged: | 2026-04-11 15:37:44 UTC; Akin |
| Author: | Akin Anarat [aut, cre] |
| Maintainer: | Akin Anarat <akin.anarat@hhu.de> |
| Repository: | CRAN |
| Date/Publication: | 2026-04-11 15:50:02 UTC |
Internal calibration data for the SSTN test
Description
These internal data files contain precomputed calibration quantities
for the Self-Similarity Test for Normality (SSTN). They include
asymptotic calibration values (mu, sigma) and asymptotic null
distributions (T), as well as sample size-specific null
distributions for the finite-sample regime.
Details
The calibration files were generated by Monte Carlo simulation and are stored as internal package data. They are not intended to be regenerated during ordinary use of the package.
The asymptotic calibration values were obtained from 10,000 Monte Carlo
simulations using the functions calibrate_mu_sigma() and
simulate_T().
The finite-sample null distributions were obtained from 10,000 Monte
Carlo simulations using the function compute_exact_T() for sample
sizes n = 2, \dots, 99.
The precomputed calibrations correspond to the default configuration
\beta = 2, M = 20, t_{\max} = 4, and H = 100.
Self-Similarity Test for Normality (SSTN)
Description
The SSTN is a statistical test for assessing whether a given sample originates from a normal distribution. It is based on the iterative application of the empirical characteristic function and comparing these estimated characteristic functions. A Monte Carlo procedure is used to obtain the empirical distribution of the test statistic under the null hypothesis.
Usage
sstn(x, verbose = FALSE)
Arguments
x |
Numeric vector of observations |
verbose |
Logical. If TRUE (default), prints a summary of the test results
including the number of summands, test statistic, and |
Value
An invisible list with the following components:
test.statistic |
Numeric. The observed value of the SSTN test statistic. |
method |
Character string indicating whether the asymptotic or the finite-sample null distribution was used. |
p.value |
Numeric. The |
Author(s)
Akin Anarat akin.anarat@hhu.de
References
Anarat, A. and Schwender, H. (2026). A test for normality based on self-similarity. arXiv preprint doi:10.48550/arXiv.2604.03810.
Examples
set.seed(123)
# Sample from standard normal (null hypothesis true)
x <- rnorm(100)
res <- sstn(x)
res$p.value
# Sample from Gamma distribution (null hypothesis false)
y <- rgamma(100, 1)
res2 <- sstn(y)
res2$p.value