Derivation of Modified Maximum Likelihood Estimators of Parameters When the Error Distribution Has Generalized Logistic Distribution
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.
Keywords
Modified Maximum Likelihood Estimators Generalized Logistic Distribution. Minimum Variance Bound Robust Estimators
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
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.
Keywords
Uyarlanmış En Çok Olabilirlik tahmin edicileri Genelleştirilmiş Lojistik Dağılımı Minimum Varyans Sınırı Robust (sağlam) tahmin ediciler
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.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistical Analysis |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | August 16, 2002 |
| Published in Issue | Year 2002 Volume: 1 Issue: 2 |
