sstn: Self-Similarity Test for Normality (SSTN)

In sstn: Self-Similarity Test for Normality

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 compares it to the characteristic function of the standard normal distribution. A Monte Carlo procedure is used to obtain the empirical distribution of the test statistic under the null hypothesis.

Usage

sstn(
  x,
  B = 500,
  grid_length = 10,
  t_max = 4,
  M_max = 100,
  beta = 0.5,
  seed = NULL,
  verbose = TRUE
)

Arguments

x	Numeric vector of observations (x_1, \dots, x_n) drawn from a distribution with finite variance. Must have length n \ge 2.
B	Integer. Number of Monte Carlo samples. Default is 500.
grid_length	Integer. Number of grid points H for the evaluation of the standardized characteristic function. Default is 10.
t_max	Positive numeric. Upper bound of the grid t_H, typically 4 to cover the effective support of the normal characteristic function. Default is 4.
M_max	Integer. Maximum number of iterations N. Default is 100.
beta	Positive numeric. Weighting parameter in the discrepancy measure. Controls the decay rate of the exponential weight \exp(-\beta t^2). Default is 0.5.
seed	Optional integer. Random seed for reproducibility of Monte Carlo samples. Default is NULL (no fixed seed).
verbose	Logical. If TRUE (default), prints a summary of the test results including the number of summands, test statistic, and p-value.

Value

An invisible list with the following components:

test_statistic	Numeric. The observed value d_{M} of the SSTN test statistic.
null_distribution	Numeric vector of length B. Test statistics from the Monte Carlo samples under the null hypothesis.
number_summands	Integer. The determined number of summands M.
p_value	Numeric. The p-value of the test.

Author(s)

Akin Anarat [e-mail]

References

Anarat A. and Schwender, H. (2025). A normality test based on self-similarity. Submitted.

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

sstn documentation built on Sept. 16, 2025, 9:11 a.m.