Görüntü Sunumu
İstatistiksel Parametre Kestirim Tekniklerinin Weibull Dağılımının Parametrelerinin Hesaplanmasında Kullanımı ve Deprem Verilerinin Weibull Dağılımına Uygulanması
Öz
Bu çalışmada istatistiksel parametre kestirim tekniklerinden "En Çok Olabilirlik Tekniği". "En Küçük Kareler Tekniği" ve Momentler Tekniği"nin Weibull Dağılımının Parametrelerinin hesaplanmasındaki kullanım anlatılmıştır. Farklı örneklem büyüklüklerinde sözü edilen teknikler içersinde hangi tekniğin daha iyi olduğunu göstermek amacı ile karşılaştırmalar yapılmış ve karşılaştırma sonuçları gözönüne alınarak deprem verilerine Weibull dağılımının bir uygulamasına yer verilmiştir.
Anahtar Kelimeler
Weibull Dağılımı En Çok Olabilirlik Tekniği En Küçük Kareler Tekniği Momentler Tekniği Deprem
Kaynakça
- A.ZENBİL El-Bashir (1991), "Estimation Techniques for A Class of Non-Regular Distributions: The Weibull Case.", Doktora Tezi, ODTÜ.
- Al- Fawzan MOHAMMAD A. (2000), “Methods for Estimating the Parameters of the Weibull Distribution", Email: mfawzan@kacst.edu.sa.
- AL-BAIDHANI, F. A., and SINCLAIR, C. D., (1987), "Comparison of Methods of Estimation of Parameters of the Weibull distribution", Communications in Statistics, Part B-- Simulation and Computation, 16, 373-384.
- ALTİNOK, Y., and KOLCAK, DEMİR, (1999), “ An Application of the Semi-Markov Model for Earthquake Occurances in North Anatolia, Turkey", Journal of the Balkan Geophysical Society, 2, 90-93.
- BURY, K.V., (1975). Statistical Models in Applied Science, John Wiley&Sons.
- CAERS, J., BEİRLANT, J. and MAES, M.A., “Statistics for Modeling Heavy Tailed Disribution in Geology", Part I and II, Mathematical Geology, 31(4): 391-410 and 411-434.
- DARGAHI, G.R., (2002), “The use Modern Statistical Theories in the Assesment of Earthquake Hazard, with Aplication to Quiet of Eastern Nort America". Soil Dynamics and Earthquake Engineering, 22, 361-369.
- ELLIS, WAYNE C., and TUMMALA, V. M. RAO, (1986), “Minimum Expected Loss Estimators of the Shape and Scale Parameters of the Weibull Distribution", IEEE. Transactions on Reliability, 35, 212-213.
- FLYGARE, MARK E., AUSTIN, JOHN A., and BUCKWALTER, ROSS M., (1985), “Maximum Likelihood Estimation for the 2-Parameter Weibull Distribution Based on Interval-Data", IEEE Transactions on Reliability, 34, 57-59.
- JEEN-HWA W., and CHIAO-HUI K., (1998), "On the Frequency Distribution of Interoccurrence Times of Earthquakes", Journal of Seismology, 2 (4): 351-358.
- JAIMYOUNG K., KYOUNGWON M., PETER J. BICKEL, P., R. RENNE, (2002), “Statistical Methods for Jointly Estimating the Decay Constant of 40K and the Age of a Dating Standard", Mathematical Geology, 34 (4): 457-474.
- KAYABALİ, K., and AKİN, M., (2003), “Seismic Hazard Map of Turkey Using the Deterministic Apporach". Engineering Geology, 69, 127-137.
- KAPPENMAN, RUSSELL F., (1985), "Estimation for the Three-Parameter Weibull, Log-Normal, and Gamma Distributions", Computational Statistics and Data Analysis, 3, 11-23.
- KOLÇAK D.- ALTINOK Y.- GÜNDOĞDU Y, “Kuzey Anadolu Fay Zonunda Weibull Olasılık Dağılımı İle Deprem Riskinin Saptanması", Deprem Araştırma Bülteni, 76. 68-79.
- LEMON, GLEN H..(1975), "Maximum Likelihood Estimation for the Three Parameter Weibull Distribution Based on Censored Samples", Technometrics, 17, 247-254.
- AMBRASEYS, N,. (1999), "The Earthquake of 10 July 1894 in the Gulf of İzmit (Turkey) and its Relation to the Earthquake of 17 August 1999". Journal of Seismology, 2 (4): 351-358.
- RIKITAKE, T.,(1975), "Statistics of Ultimate Strain of the Earts Crust's and Probability of Earthquake Occurance", Tectonophysics, Vol. 26, 1-21.
- RIKITAKE, T. ,(1999), "Probability of a Great Earthquake to Recur in the Tokai District, Japan: Revaluation Based on Newly-Developed Paleoseismology, Plate Tectonics, Tsunami Study, Micro-Seismicity and Geodetic Measurements". Earth Planets Space, 51, 147-157.
- SERGIO, G.,F., (2003), “Probabilistic Prediction of the Next Large Earhquake in the Michoacan Fault-Segment of the Mexican Subduction Zone", Geofisica Internacional, 42, 69-81.
- SERGIO, G., F., (2003), "The Conditional Probability of Earthquake Occurrence and the Next Large Earthquake in Tokyo, Japan, "Journal of Seismology ,7 (2): 145-153.
- SINHA, S. K., (1987), "Bayesian Estimation of the Parameters and Reliability Function of a Mixture of Weibull Life Distributions", Journal of Statistical Planning and Inference, 16 377-387.
- ŞAHİN S. (2000) "İstatistiksel Kalite Kontrolünde Üstel ve Weibull Dağılımların X-Kontrol Grafiklerine Uygulanması Üzerine Teorik Bir Yaklaşım", Doktora Tezi- Cumhuriyet Üniversitesi.
- V. F. PISARENKO and A. A. LYUBUSHIN, (1997), “Statistical Estimation of Maximum Peak Ground Acceleration at a Given Point of a Seismic Region, “Journal of Seismology, I (4): 395-405.
- W.Q. MEEKER and L.A. ESCOBAR, (1995), Statistical Methods for Reliability, John Wiley&Sons.
- ZANAKIS, STELIOS H., and KYPARISIS, J., (1986), “A Review of Maximum Likelihood Estimation Methods for the Three-Parameter Weibull Distribution", Journal of Statistical Computation and Simulation, 25, 53-73.
The Use of Statistical Parameter Estimation Methods in the Calculation of the Parameters Weibull Distribution and the Application of Weibull Distribution to Earthquake Data
Öz
In this study, “Maximum Likelihod Method", “Least Squares Method” and “Method of Moments” which are the statistical parameter estimation methods of use in the calculation of the parameters Weibull distribution is being explained. We compare this methods in different sample sizes to show which one is the best and the results of this compare is used to apply the weibull distribution to earthquake dates.
Anahtar Kelimeler
Weibull Distibution Maximum Likelihod Method Least Squares Method Method of Moments Earthquake
Kaynakça
- A.ZENBİL El-Bashir (1991), "Estimation Techniques for A Class of Non-Regular Distributions: The Weibull Case.", Doktora Tezi, ODTÜ.
- Al- Fawzan MOHAMMAD A. (2000), “Methods for Estimating the Parameters of the Weibull Distribution", Email: mfawzan@kacst.edu.sa.
- AL-BAIDHANI, F. A., and SINCLAIR, C. D., (1987), "Comparison of Methods of Estimation of Parameters of the Weibull distribution", Communications in Statistics, Part B-- Simulation and Computation, 16, 373-384.
- ALTİNOK, Y., and KOLCAK, DEMİR, (1999), “ An Application of the Semi-Markov Model for Earthquake Occurances in North Anatolia, Turkey", Journal of the Balkan Geophysical Society, 2, 90-93.
- BURY, K.V., (1975). Statistical Models in Applied Science, John Wiley&Sons.
- CAERS, J., BEİRLANT, J. and MAES, M.A., “Statistics for Modeling Heavy Tailed Disribution in Geology", Part I and II, Mathematical Geology, 31(4): 391-410 and 411-434.
- DARGAHI, G.R., (2002), “The use Modern Statistical Theories in the Assesment of Earthquake Hazard, with Aplication to Quiet of Eastern Nort America". Soil Dynamics and Earthquake Engineering, 22, 361-369.
- ELLIS, WAYNE C., and TUMMALA, V. M. RAO, (1986), “Minimum Expected Loss Estimators of the Shape and Scale Parameters of the Weibull Distribution", IEEE. Transactions on Reliability, 35, 212-213.
- FLYGARE, MARK E., AUSTIN, JOHN A., and BUCKWALTER, ROSS M., (1985), “Maximum Likelihood Estimation for the 2-Parameter Weibull Distribution Based on Interval-Data", IEEE Transactions on Reliability, 34, 57-59.
- JEEN-HWA W., and CHIAO-HUI K., (1998), "On the Frequency Distribution of Interoccurrence Times of Earthquakes", Journal of Seismology, 2 (4): 351-358.
- JAIMYOUNG K., KYOUNGWON M., PETER J. BICKEL, P., R. RENNE, (2002), “Statistical Methods for Jointly Estimating the Decay Constant of 40K and the Age of a Dating Standard", Mathematical Geology, 34 (4): 457-474.
- KAYABALİ, K., and AKİN, M., (2003), “Seismic Hazard Map of Turkey Using the Deterministic Apporach". Engineering Geology, 69, 127-137.
- KAPPENMAN, RUSSELL F., (1985), "Estimation for the Three-Parameter Weibull, Log-Normal, and Gamma Distributions", Computational Statistics and Data Analysis, 3, 11-23.
- KOLÇAK D.- ALTINOK Y.- GÜNDOĞDU Y, “Kuzey Anadolu Fay Zonunda Weibull Olasılık Dağılımı İle Deprem Riskinin Saptanması", Deprem Araştırma Bülteni, 76. 68-79.
- LEMON, GLEN H..(1975), "Maximum Likelihood Estimation for the Three Parameter Weibull Distribution Based on Censored Samples", Technometrics, 17, 247-254.
- AMBRASEYS, N,. (1999), "The Earthquake of 10 July 1894 in the Gulf of İzmit (Turkey) and its Relation to the Earthquake of 17 August 1999". Journal of Seismology, 2 (4): 351-358.
- RIKITAKE, T.,(1975), "Statistics of Ultimate Strain of the Earts Crust's and Probability of Earthquake Occurance", Tectonophysics, Vol. 26, 1-21.
- RIKITAKE, T. ,(1999), "Probability of a Great Earthquake to Recur in the Tokai District, Japan: Revaluation Based on Newly-Developed Paleoseismology, Plate Tectonics, Tsunami Study, Micro-Seismicity and Geodetic Measurements". Earth Planets Space, 51, 147-157.
- SERGIO, G.,F., (2003), “Probabilistic Prediction of the Next Large Earhquake in the Michoacan Fault-Segment of the Mexican Subduction Zone", Geofisica Internacional, 42, 69-81.
- SERGIO, G., F., (2003), "The Conditional Probability of Earthquake Occurrence and the Next Large Earthquake in Tokyo, Japan, "Journal of Seismology ,7 (2): 145-153.
- SINHA, S. K., (1987), "Bayesian Estimation of the Parameters and Reliability Function of a Mixture of Weibull Life Distributions", Journal of Statistical Planning and Inference, 16 377-387.
- ŞAHİN S. (2000) "İstatistiksel Kalite Kontrolünde Üstel ve Weibull Dağılımların X-Kontrol Grafiklerine Uygulanması Üzerine Teorik Bir Yaklaşım", Doktora Tezi- Cumhuriyet Üniversitesi.
- V. F. PISARENKO and A. A. LYUBUSHIN, (1997), “Statistical Estimation of Maximum Peak Ground Acceleration at a Given Point of a Seismic Region, “Journal of Seismology, I (4): 395-405.
- W.Q. MEEKER and L.A. ESCOBAR, (1995), Statistical Methods for Reliability, John Wiley&Sons.
- ZANAKIS, STELIOS H., and KYPARISIS, J., (1986), “A Review of Maximum Likelihood Estimation Methods for the Three-Parameter Weibull Distribution", Journal of Statistical Computation and Simulation, 25, 53-73.
Toplam 25 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | İstatistiksel Analiz, Nicel Karar Yöntemleri |
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Yayımlanma Tarihi | 17 Ağustos 2003 |
| Yayımlandığı Sayı | Yıl 2003 Cilt: 2 Sayı: 2 |
