A model for bimodal rates and proportions

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Vila R., Alfaia L., Menezes A. F., ÇANKAYA M. N., Bourguignon M.

Journal of Applied Statistics, cilt.51, sa.4, ss.664-681, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1080/02664763.2022.2146661
  • Dergi Adı: Journal of Applied Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Business Source Elite, Business Source Premier, CAB Abstracts, Veterinary Science Database, zbMATH
  • Sayfa Sayıları: ss.664-681
  • Anahtar Kelimeler: beta distribution, Bimodal model, bimodality, bounded data, maximum likelihood, regression model
  • Uşak Üniversitesi Adresli: Evet

Özet

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution, such as bimodality, real moments, entropies and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.