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Derivation of Modified Maximum Likelihood Estimators of Parameters When the Error Distribution Has Generalized Logistic Distribution

Year 2002, Volume: 1 Issue: 2, 55 - 63, 16.08.2002

Abstract

The estimators of parameters in the model
Yi = μ + ei (1 ≤ i ≤n )
will be derived when the error distribution has Generalized Logistic distribution and the methodology explained in this study will be supported with an example (Şenoğlu, 2000).

In our future studies, the estimators of the parameters in the models used commonly in statistical design of experiments such as Balanced Incomplete Block Design, Latin Square Design and Factorial Design etc. will be derived by using the methodology given in the following sections. This methodology is the basic of our future studies that is why we investigate it in detail.

References

  • BARNETT, V.D. (1996), Evoluation of the maximum likelihood estimator where the likelihood equation has multiple roots. Biometrika 53, 153-165.
  • BARTLETT, M.S. (1953) Approximate confidence intervals, Biometrika 40, 12-19.
  • HUBER, P.J. (1981), Robust Statistics. New York: John Wiley.
  • ISLAM, M.Q. TİKU, M.L. and YILDIRIM, F. (1999), Nonnormal regression with skew distributions. Commun. Stat.- Theory Meth. (submitted for publication).
  • ŞENOĞLU, B. (2000), Experimental design under nonnormality, Ph. D. Thesis, METU.
  • TAN, W.Y. and TİKU, M.L. (1999), Sampling Distributions in Terms of Laguerre Polynomials and Aplications, New Delhi: John Wiley Eastern.
  • TİKU, M.L. (1967), Estimating the mean and standart deviation from censored normal samples. Biometrika 54, 155-165.
  • TİKU, M.L. (1968), Estimating the parameters of log-normal distribution from censored samples. J. Amer. Stat Assoc. 63, 134-140.
  • TİKU, M.L. TAN, W.Y., and BALAKRİSHNAN, N. (1986), Robust Inference. New York: Marcel Dekker.
  • VAUGHAN, D.C. (1992). On the Tiku-Suresh method of estimation. Commun. Stat.-Theory Meth. 21, 391-404.

Hata Terimlerinin Genelleştirilmiş Lojistik Dağılıma Sahip Olması Durumunda Parametrelerin Uyarlanmış En Çok Olabilirlik Tahmin Edicilerinin Bulunması

Year 2002, Volume: 1 Issue: 2, 55 - 63, 16.08.2002

Abstract

Hata terimlerinin Genelleştirilmiş Lojistik dağılıma sahip olması durumunda;
yi = μ + ei (1≤ i ≤ n)
modelindeki parametrelerin tahmin edicileri bulunacak ve bu aşamada izlenecek metodoloji bir uygulama ile desteklenecektir (Şenoğlu, 2000).

Söz konusu metodolojiye dayanan ilerleyen çalışmalarımızda aşağıda detayları verilen metodoloji kullanılarak Dengeli Eksik Bölük Tasarımları, Latin Kareleri ve Faktöriyel Tasarımlar vb. Deney Tasarımında yaygın olarak kullanılan tasarımlardaki parametrelerin tahmin edicileri bulunacak ve elde edilen sonuçlar ayrıca değerlendirilecektir. Sözü edilen metodolojinin burada detaylı olarak incelenmesinin başlıca amacı, ilerideki çalışmalarımızın temelini oluşturmasıdır.

References

  • BARNETT, V.D. (1996), Evoluation of the maximum likelihood estimator where the likelihood equation has multiple roots. Biometrika 53, 153-165.
  • BARTLETT, M.S. (1953) Approximate confidence intervals, Biometrika 40, 12-19.
  • HUBER, P.J. (1981), Robust Statistics. New York: John Wiley.
  • ISLAM, M.Q. TİKU, M.L. and YILDIRIM, F. (1999), Nonnormal regression with skew distributions. Commun. Stat.- Theory Meth. (submitted for publication).
  • ŞENOĞLU, B. (2000), Experimental design under nonnormality, Ph. D. Thesis, METU.
  • TAN, W.Y. and TİKU, M.L. (1999), Sampling Distributions in Terms of Laguerre Polynomials and Aplications, New Delhi: John Wiley Eastern.
  • TİKU, M.L. (1967), Estimating the mean and standart deviation from censored normal samples. Biometrika 54, 155-165.
  • TİKU, M.L. (1968), Estimating the parameters of log-normal distribution from censored samples. J. Amer. Stat Assoc. 63, 134-140.
  • TİKU, M.L. TAN, W.Y., and BALAKRİSHNAN, N. (1986), Robust Inference. New York: Marcel Dekker.
  • VAUGHAN, D.C. (1992). On the Tiku-Suresh method of estimation. Commun. Stat.-Theory Meth. 21, 391-404.
There are 10 citations in total.

Details

Primary Language Turkish
Subjects Statistical Analysis
Journal Section Research Articles
Authors

Birdal Şenoğlu

Hülya Şen

Publication Date August 16, 2002
Published in Issue Year 2002 Volume: 1 Issue: 2

Cite

APA Şenoğlu, B., & Şen, H. (2002). Hata Terimlerinin Genelleştirilmiş Lojistik Dağılıma Sahip Olması Durumunda Parametrelerin Uyarlanmış En Çok Olabilirlik Tahmin Edicilerinin Bulunması. İstatistik Araştırma Dergisi, 1(2), 55-63.