Cebeci Z., Ceritoğlu F., Çelik Güney M., Ünalan A.
SYMMETRY, vol.18, no.3, pp.1-44, 2026 (SCI-Expanded, Scopus)
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Publication Type:
Article / Article
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Volume:
18
Issue:
3
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Publication Date:
2026
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Doi Number:
10.3390/sym18030458
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Journal Name:
SYMMETRY
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Journal Indexes:
Scopus, Science Citation Index Expanded (SCI-EXPANDED), INSPEC, zbMATH
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Page Numbers:
pp.1-44
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Çukurova University Affiliated:
Yes
Abstract
This study proposes Optimized Skewness and Kurtosis Transformation (OSKT), a novel moment-targeting normality transformation that corrects asymmetry and peakedness in non-normal data. OSKT employs a transformation function derived from the Tukey g–h distribution, incorporating skewness and kurtosis parameters, and is optimized by minimizing a single objective function based on the Anderson–Darling test statistic. The optimization process uses L-BFGS-B to tune the transformation parameters to find the best fit for the standard normal distribution. OSKT ensures a balance between symmetry and tail behavior by minimizing deviations from theoretical normality. It has highly competitive performance compared to the alternative, Box–Cox, Yeo–Johnson transformations, including their robust variants and moment-matching Lambert W method, for normalizing complex distributions. According to our analysis, OSKT also achieves superior normalization for highly non-Gaussian data, successfully transforming highly resistant distributions, including approximately symmetric bimodal datasets, where other methods fail.