A Moment-Targeting Normality Transformation Based on Simultaneous Optimization of Tukey g–h Distribution Parameters


Cebeci Z., Ceritoğlu F., Çelik Güney M., Ünalan A.

SYMMETRY, cilt.18, sa.3, ss.1-44, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3390/sym18030458
  • Dergi Adı: SYMMETRY
  • Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), INSPEC, zbMATH
  • Sayfa Sayıları: ss.1-44
  • Çukurova Üniversitesi Adresli: Evet

Özet

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.