Comparative Inference for the Cubic Rank Transmuted Inverse Weibull Distribution Based on Maximum Likelihood and Least Squares Methods

Köksal Babacan E., Kaya S.

VII. International Applied Statistics Congress (UYIK – 2026), İstanbul, Türkiye, 11 - 13 Mayıs 2026, ss.175, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.175
  • Ankara Üniversitesi Adresli: Evet

Özet

Identifying statistical distributions that adequately fit real-world data is essential for understanding the underlying characteristics of populations across diverse fields such as economics, medicine, social sciences, and engineering. Although numerous statistical distributions have been proposed in the literature for modeling real data, the increasing diversity of data types has created a growing need for more flexible models capable of capturing complex data structures. Consequently, various methods have been developed in recent years to construct new statistical distributions. In this study, the Cubic Rank Transmuted Inverse Weibull (CRTIW) distribution, obtained via the cubic rank transmutation method, is investigated. Due to its flexibility in modeling lifetime data with different hazard rate shapes, the CRTIW distribution serves as a strong alternative to classical lifetime models. The model parameters are estimated using maximum likelihood and least squares estimation methods. The performance of the estimators is evaluated in terms of bias and mean squared error. For this purpose, an extensive Monte Carlo simulation study is conducted under various parameter settings and sample sizes. The simulation results indicate that the maximum likelihood estimators perform satisfactorily for moderate and large sample sizes, whereas noticeable deviations may occur in small samples. Finally, the practical applicability of the CRTIW distribution is demonstrated through applications to real-world datasets. The empirical findings suggest that the proposed model provides an effective and competitive alternative for modeling lifetime data.