A Closed-Form Alternative for the Frequency Distribution of Stably Distributed Random Components in Daily-Mean Self-Potential (SP) Time Series: Example from Urla Station, Turkey

Sındırgı P.

Pure and Applied Geophysics, cilt.180, sa.7, ss.2827-2840, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 180 Sayı: 7
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00024-023-03302-1
  • Dergi Adı: Pure and Applied Geophysics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Compendex, Geobase, INSPEC
  • Sayfa Sayıları: ss.2827-2840
  • Anahtar Kelimeler: exponentiated-exponential cauchy (EEC) distributions, model selection and multimodel inference, Self-potential, stable distribution
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

The author of this paper has recently shown that daily-mean self-potential (SP) time series recorded at Urla station, Turkey, exhibit a unit-root nonstationary behavior with weakly correlated stationary differences driven by stable noise of tail index around 1.12–1.15. This work mainly aims to assess whether the Exponentiated-Exponential Cauchy (EEC) family distributions could be utilized as an alternative to the stable distributions. The EEC family distributions have many advantages as they have closed-form representations. Those goodness-of-fit statistics, relative strengths and predictive abilities of the three EEC family distributions with two- (Cauchy), three- (EEC-3) and four (EEC-4) parameters were compared with that of the stable one. The Akaike Information Criterion (AIC)-based relative strength for the EEC-3 candidate indicated that it is approximately 1.85 times more likely to be the best approximating model than the stable one. Additionally, those considerably smaller relative mean absolute errors (RMAE) for the EEC-3 model indicated that the asymptotic tail properties of the empirical distribution could be better represented in comparison with the stable model. The results of this work revealed, on the example of Urla, that an EEC-3 distribution would plausibly the stable one. We hope the findings of this paper would provide many advantages and facilitate the numerical computations in solving problems arising from the use of stable laws.