Statistical inference for alpha-series process with the inverse Gaussian distribution

Kara M., TÜRKŞEN Ö., AYDOĞDU H.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, cilt.46, sa.6, ss.4938-4950, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 6
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/03610918.2016.1139127
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4938-4950
  • Anahtar Kelimeler: alpha-Series process, Asymptotic normality, Inverse Gaussian distribution, Maximum likelihood estimate, Modified moment estimate
  • Ankara Üniversitesi Adresli: Evet

Özet

Statistical inferences for the geometric process (GP) are derived when the distribution of the first occurrence time is assumed to be inverse Gaussian (IG). An alpha-series process, as a possible alternative to the GP, is introduced since the GP is sometimes inappropriate to apply some reliability and scheduling problems. In this study, statistical inference problem for the alpha-series process is considered where the distribution of first occurrence time is IG. The estimators of the parameters alpha, mu, and sigma(2) are obtained by using the maximum likelihood (ML) method. Asymptotic distributions and consistency properties of the ML estimators are derived. In order to compare the efficiencies of the ML estimators with the widely used nonparametric modified moment (MM) estimators, Monte Carlo simulations are performed. The results showed that the ML estimators are more efficient than the MM estimators. Moreover, two real life datasets are given for application purposes.