KaydedilenlerDerginizi ekleyin

Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Cilt: 69 - Sayı: 1

A comparison of different methods of estimation for the flexible Weibull distribution

Sajid ALİ
Sanku DEY
M H TAHİR
Muhammad MANSOOR
Sayfa
794–814
Yayın Tarihi
2020-06-30
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A real data example is also a part of this work.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This article presents different parameter estimation methods for flexible Weibull distribution introduced by Bebbington et al. (Reliability Engineering and System Safety 92:719-726, 2007), which is a modified version of the Weibull distribution and is suitable to model different shapes of the hazard rate.
📊
Temel Bulgular & Veri:We consider both frequentist and Bayesian estimation methods and present a comprehensive comparison of them.
💡
Sonuç & Katkı:A real data example is also a part of this work.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:2007 Verileri
⚙️Değişkenler:Weibull distribution · maximum likelihood estimators · least square estimators

Abstract

This article presents different parameter estimation methods for flexible Weibull distribution introduced by Bebbington et al. (Reliability Engineering and System Safety 92:719-726, 2007), which is a modified version of the Weibull distribution and is suitable to model different shapes of the hazard rate. We consider both frequentist and Bayesian estimation methods and present a comprehensive comparison of them. For frequentist estimation, we consider the maximum likelihood estimators, least squares estimators, weighted least squares estimators, percentile estimators, the maximum product spacing estimators, the minimum spacing absolute distance estimators, the minimum spacing absolute log-distance estimators, Cramér von Mises estimators, Anderson Darling estimators, and right tailed Anderson Darling estimators, and compare them using a comprehensive simulation study. We also consider Bayesian estimation by assuming gamma priors for both shape and scale parameters. We use a Markov Chain Monte Carlo algorithm to compute the posterior summaries. A real data example is also a part of this work.

🔖

Bu Makaleye Atıf Yap

ALİ, S., DEY, S., TAHİR, M. H., MANSOOR, M. (2020). A comparison of different methods of estimation for the flexible Weibull distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 69 - Sayı: 1, 794–814. https://ajindex.com/articles/746875

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (13)

  1. Bebbington, M., Lai, C.-D., and Zitikis, R. (2007). A flexible weibull extension. Reliability Engineering &System Safety, 92(6):719-726.
  2. Devroye, L. (1986). Non-Uniform Random Variate Generation. Springer-Verlag. Kao, J. H. K. (1959). A graphical estimation of mixed Weibull parameters in life-testing of electron tubes.Technometrics, 1(4):389-407.
  3. Kenney, J. and Keeping, E. (1962). Mathematics of statistics. Number v. 2 in Mathematics of Statistics.Princeton: Van Nostrand. Mann, N., Schafer, R., and Singpurwalla, N. (1974). Methods for statistical analysis of reliability and lifedata. Wiley. Moors, J. J. A. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society. Series D(The Statistician), 37(1):25-32.
  4. Nadarajah, S. and Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6):543-558.
  5. Shaked, M. and Shanthikumar, J. (2007). Stochastic Orders. Springer New York. Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain goodness of fit criteria based on stochastic processes. The Annals of Mathematical Statistics, 23(2):193-212.
  6. Anderson, T. W. and Darling, D. A. (1954). A test of goodness of fit. Journal of the American Statistical Association, 49(268):765-769.
  7. Cheng, R. C. H. and Amin, N. A. K. (1979). Maximum product of spacings estimation with application to the lognormal distribution, math. Cheng, R. C. H. and Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society. Series B (Methodological), 45(3):394-403.
  8. Pettitt, A. N. (1976). A two-sample Anderson-Darling rank statistic. Biometrika, 63(1):161-168.
  9. Dey, S., Al-Zahrani, B., and Basloom, S. (2017a). Dagum distribution: Properties and different methods of estimation. International Journal of Statistics and Probability, 6(2):74-92.
  10. Dey, S., Ali, S., and Park, C. (2015). Weighted exponential distribution: properties and different methods of estimation. Journal of Statistical Computation and Simulation, 85(18):3641-3661.
  11. Dey, S., Dey, T., Ali, S., and Mulekar, M. S. (2016). Two-parameter Maxwell distribution: Properties and different methods of estimation. Journal of Statistical Theory and Practice, 10(2):291-310.
  12. Dey, S., Dey, T., and Kundu, D. (2014). Two-parameter Rayleigh distribution: Different methods of estimation. American Journal of Mathematical and Management Sciences, 33(1):55-74.
  13. Dey, S., Kumar, D., Ramos, P. L., and Louzada, F. (2017