Abstract
Discriminant analysis is defined as a statistical technique that
classifies a unit whose properties are measured, into one of the known finite
numbers of populations. In this classifying process, an error occurs when the
unit is classified to different population from its own population. This error
is called the error rate or the probability of incorrect classification. It is
desirable to minimize this error. This study focuses on determining the
parameter estimation method that provides the minimum error rate, when the
parameters of Weibull populations are not known. Maximum likelihood (ML),
moments (MOM) and least squares (LS) methods are chosen from among parameter
estimation methods. How the error rate is affected by parameter estimators ML,
MOM and LS is examined with the simulation study.
References
- P. A. Lachenburch, “Discriminant Analysis”, New York, Hafner, 1975.
- G. A. F. Seber, “Multivariate Observations”, New York, John Wiley & Sons. Inc, 1984.
- T.W.Anderson, “Introduction to Multivariate Statistical Analysis”, Wiley, New York, 1984.
- B. L. Welch, “Note on Discriminant Functions”, Biometrika, 31, 218–220, 1939.
- P. A. Lachenburch and R. Mickey, “Estimation of Error Rates in Discriminant Analysis”, Technometrics, 10, 1–11, 1968.
- S. M. Snapin,” An Evaluation of Smooted Error Rate Estimators in Discriminant Analysis”, Institute of Statistics Miemeo Series, Chapel Hill, 1983.
- M. Hills, “Allocation Rules and Their Error Rates”, J. Roy. Stat. Soc. B, 28, 1-31, 1966.
- H. D. Biçer, “Discriminant analiysis in censored data: Weibull distribution case”, Doctoral dissertation, University of Ankara, 2011.
- C. A. B. Smith, “Some Examples of Discrimination”, Annals of Eugenics, 18, 272-282, 1978.
- N. L. Johnson, S. Kotz and N. Balakrishnan,“Continuous univariate distributions”, New York, Wiley, 1995.
- M. Tiryakioğlu and D. Hudak,“Unbiased estimates of the Weibull parameters by the linear regression method”,Journal of Materials Science, 43, 1914-1919, 2008.
Abstract
Diskriminant analizi, özellikleri ölçülen bir birimi, bilinen sonlu
sayıdaki kitlelerden birine sınıflandıran istatistiksel bir teknik olarak
tanımlanır. Bu sınıflandırma işleminde, birim kendi kitlesinden farklı kitleye
sınıflandırıldığında bir hata meydana gelir. Bu hata, hata oranı veya yanlış
sınıflandırma olasılığı olarak adlandırılır. Arzu edilen bu hatayı minimum
yapmaktır. Bu çalışmada Weibull dağılımlı kitlelerde parametrelerin bilinmediği
durumda, minumum hata oranıyla atama yapan parametre tahmin yönteminin
belirlenmesi üzerinde durulmaktadır. Parametre tahmin yöntemlerinden; en çok
olabilirlik (ML), moment (MOM) ve en küçük kareler (LS) yöntemi seçilmiştir.
Simülasyon çalışması ile hata olasılığının ML, MOM ve LS parametre tahmin
edicilerinden nasıl etkilendiği incelenmiştir.
References
- P. A. Lachenburch, “Discriminant Analysis”, New York, Hafner, 1975.
- G. A. F. Seber, “Multivariate Observations”, New York, John Wiley & Sons. Inc, 1984.
- T.W.Anderson, “Introduction to Multivariate Statistical Analysis”, Wiley, New York, 1984.
- B. L. Welch, “Note on Discriminant Functions”, Biometrika, 31, 218–220, 1939.
- P. A. Lachenburch and R. Mickey, “Estimation of Error Rates in Discriminant Analysis”, Technometrics, 10, 1–11, 1968.
- S. M. Snapin,” An Evaluation of Smooted Error Rate Estimators in Discriminant Analysis”, Institute of Statistics Miemeo Series, Chapel Hill, 1983.
- M. Hills, “Allocation Rules and Their Error Rates”, J. Roy. Stat. Soc. B, 28, 1-31, 1966.
- H. D. Biçer, “Discriminant analiysis in censored data: Weibull distribution case”, Doctoral dissertation, University of Ankara, 2011.
- C. A. B. Smith, “Some Examples of Discrimination”, Annals of Eugenics, 18, 272-282, 1978.
- N. L. Johnson, S. Kotz and N. Balakrishnan,“Continuous univariate distributions”, New York, Wiley, 1995.
- M. Tiryakioğlu and D. Hudak,“Unbiased estimates of the Weibull parameters by the linear regression method”,Journal of Materials Science, 43, 1914-1919, 2008.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 1, 2018 |
| Submission Date | August 10, 2017 |
| Acceptance Date | March 20, 2018 |
| Published in Issue | Year 2018 Volume: 22 Issue: 6 |
Cite
Sakarya University Journal of Science (SAUJS)