KaydedilenlerDerginizi ekleyin

Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2024 / Volume: 73 Issue: 4

Bias corrected maximum likelihood estimators for the parameters of the generalized normal distribution

Hasan Hüseyin Gül(GIRESUN UNIVERSITY)0000-0001-9905-8605
Fatma Zehra Doğru(GIRESUN UNIVERSITY)0000-0001-8220-2375
Sayfa
—
Yayın Tarihi
2024-12-30
🏛️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)

Finally, a real data example is presented to illustrate the application of methods.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The generalized normal (GN) distribution was defined as a generalization of the normal, Laplace, and uniform distributions, with extensive application areas modeling different data settings.
📊
Temel Bulgular & Veri:This article adopts the bias-corrected approach, following the analytical methodology suggested by Cox and Snell [1].
💡
Sonuç & Katkı:Finally, a real data example is presented to illustrate the application of methods.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bootstrap bias-correction · Cox-Snell bias-correction · generalized normal distribution

Abstract

The generalized normal (GN) distribution was defined as a generalization of the normal, Laplace, and uniform distributions, with extensive application areas modeling different data settings. At the same time, its maximum likelihood estimators (MLEs) are biased in finite samples. Since such biases may affect the accuracy of estimates, we consider constructing unbiased estimators for unknown parameters of GN distribution. This article adopts the bias-corrected approach, following the analytical methodology suggested by Cox and Snell [1]. Additionally, we explore both regular biases and parametric Bootstrap bias correction techniques. A comprehensive Monte Carlo simulation is conducted to compare the performances of these estimators in estimating GN parameters. Finally, a real data example is presented to illustrate the application of methods.

🔖

Bu Makaleye Atıf Yap

Gül, H. H., Doğru, F. Z. (2024). Bias corrected maximum likelihood estimators for the parameters of the generalized normal distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 4. https://doi.org/10.31801/cfsuasmas.1439744

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (33)

  1. Cox, D. R., Snell, E. J., A general definition of residuals, Journal of the Royal Statistical Society: Series B (Methodological), 30(2) (1968), 248-265. https://doi.org/10.1111/j.2517-6161.1968.tb00724.x
  2. Briasouli, A., Tsakalides, P., Stouraitis, A., Hidden messages in heavy tails: DCT-Domain watermark detection using AlphaStable models, IEEE Trans, 7(4) (2005), 700-715. https://doi.org/10.1109/TMM.2005.850970
  3. Kokkinakis, K., Nandi, A., Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling, Signal Processing, 85 (2005), 1852-1858. https://doi.org/10.1016/j.sigpro.2005.02.017
  4. Sharifi, K., Leon-Garcia, A., Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video, IEEE Transactions on Circuits and Systems for Video Technology, 5(1) (1995), 52-56. https://doi.org/10.1109/76.350779
  5. Choi, S., Cichocki, A., Amari, S., Flexible independent component analysis. In Neural Networks for Signal Processing 8, Proceedings of the 1998 IEEE Signal Processing Society Workshop, (1998), 83-92. https://doi.org/10.1023/A:1008135131269
  6. Wu, H. C., Principe, J., Minimum entropy algorithm for source separation, In 1998 Midwest Symposium on Circuits and Systems, Notre Dame, USA, (1998), 242-245. https://doi.org/10.1109/MWSCAS.1998.759478
  7. Subbotin, M. T., On the Law of Frequency of Error, Maths Books, 31(2) (1923), 206-301. http://mi.mathnet.ru/sm6854
  8. Nadarajah, S., A generalized normal distribution, Journal of Applied Statistics, 32(7) (2005), 685-694. https://doi.org/10.1080/02664760500079464
  9. Varanasi, M. K., Aazhang, B., Parametric generalized Gaussian density estimation. Journal of the Acoustical Society of America, 86(4) (1989), 1404-1415. https://doi.org/10.1121/1.398700
  10. Roenko, A. A., Lukin, V. V., Djurovc, I., Simeunovic, M., Estimation of parameters for generalized Gaussian distribution, In 2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP), IEEE, (2014), 376-379. https://doi.org/10.1109/ISCCSP.2014.6877892
  11. Eskin, E. N., Joint Modelling of the Location and Scale Parameters of the Generalized Normal Distribution, Master’s Thesis, Giresun University, Giresun, Turkey, (2022).
  12. Eskin, E. N., Doğru, F. Z., A heteroscedastic regression model with the generalized normal distribution, Sigma Journal of Engineering and Natural Sciences, in press, 42(5) (2024), 1480-1489. https://sigma.yildiz.edu.tr/article/1673 doi:10.14744/sigma.2024.00114
  13. Efron, B., The jackknife, the bootstrap and other resampling plans, Society for Industrial and Applied Mathematics, (1982). https://doi.org/10.1137/1.9781611970319
  14. Efron, B., Tibshirani, R. J., An Introduction to the Bootstrap, Volume 57 of Monographs on Statistics and Applied Probability, Chapman and Hall, New York, 1994. https://doi.org/10.1201/9780429246593
  15. Cordeiro, G. M., Da Rocha, E. C., Da Rocha, J. G. C., Cribari-Neto, F., Bias-corrected maximum likelihood estimation for the beta distribution, Journal of Statistical Computation and Simulation, 58(1) (1997), 21-35. https://doi.org/10.1080/00949659708811820
  16. Saha, K., Paul, S., Bias-corrected maximum likelihood estimator of the negative binomial dispersion parameter, Biometrics, 61(1) (2005), 179-185. https://doi.org/10.1111/j.0006-341X.2005.030833.x
  17. Lemonte, A. J., Cribari-Neto, F., Vasconcellos, K. L., Improved statistical inference for the two-parameter Birnbaum–Saunders distribution, Computational Statistics and Data Analysis, 51(9) (2007), 4656-4681. https://doi.org/10.1016/j.csda.2006.08.016
  18. Giles, D. E., Feng, H., Bias of the maximum likelihood estimators of the two-parameter gamma distribution revisited, Econometrics Working Paper EWP0906, Department of Economics, University of Victoria, 2009. https://ideas.repec.org/p/vic/vicewp/0908.html
  19. Lemonte, A. J., Improved point estimation for the Kumaraswamy distribution, Journal of Statistical Computation and Simulation, 81(12) (2011), 1971-1982. https://doi.org/10.1080/00949655.2010.511621
  20. Giles, D. E., A note on improved estimation for the Topp-Leone distribution, Econometrics Working Paper EWP1203, Department of Economics, University of Victoria, 2012. https://ideas.repec.org/p/vic/vicewp/1703.html
  21. Giles, D. E., Feng, H., Godwin, R. T., On the bias of the maximum likelihood estimator for the two-parameter Lomax distribution, Communications in Statistics-Theory and Methods, 42(11) (2013), 1934-1950. https://doi.org/10.1080/03610926.2011.600506
  22. Schwartz, J., Godwin, R. T., Giles, D. E., Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution, Journal of Statistical Computation and Simulation, 83(3) (2013), 434-445. https://doi.org/10.1080/00949655.2011.615316
  23. Zhang, G., Liu, R., Bias-corrected estimators of scalar skew normal, In New Developments in Statistical Modeling, Inference and Application, Springer, Cham, (2016), 203-214. https://doi.org/10.1007/978-3-319-42571-9_11
  24. Schwartz, J., Giles, D. E., Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution, Communications in Statistics-Theory and Methods, 45(2) (2016), 465-478. https://doi.org/10.1080/03610926.2013.824590
  25. Wang, M., Wang, W., Bias-corrected maximum likelihood estimation of the parameters of the weighted Lindley distribution, Communications in Statistics-Simulation and Computation, 46(1) (2017), 530-545. https://doi.org/10.1080/03610918.2014.970696
  26. Reath, J., Dong, J., Wang, M., Improved parameter estimation of the log-logistic distribution with applications, Computational Statistics, 33(1) (2018), 339-356. https://doi.org/10.1007/s00180-017-0738-y
  27. Mazucheli, J., Dey, S., Bias-corrected maximum likelihood estimation of the parameters of the generalized half-normal distribution, Journal of Statistical Computation and Simulation, 88(6) (2018), 1027-1038. https://doi.org/10.1080/00949655.2017.1413649
  28. Mazucheli, J., Menezes, A. F. B., Dey, S., Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution, Communications in Statistics-Theory and Methods, 47(15) (2018), 3767-3778. https://doi.org/10.1080/03610926.2017.1361993
  29. Mazucheli, J., Menezes, A. F. B., Dey, S., Bias-corrected maximum likelihood estimators of the parameters of the inverse Weibull distribution, Communications in Statistics-Simulation and Computation, 48(7) (2019), 2046-2055. https://doi.org/10.1080/03610918.2018.1433838
  30. Menezes, A. F. B., Mazucheli, J., Improved maximum likelihood estimators for the parameters of the Johnson SB distribution, Communications in Statistics-Simulation and Computation, 49(6) (2020), 1511-1526. https://doi.org/10.1080/03610918.2018.1498892
  31. Menezes, A., Mazucheli, J., Alqallaf, F., Ghitany, M. E., Bias-corrected maximum likelihood estimators of the parameters of the Unit-Weibull distribution, Austrian Journal of Statistics, 50(3) (2021), 41-53. https://doi.org/10.17713/ajs.v50i3.1023
  32. Cordeiro, G. M., Klein, R., Bias correction in ARMA models, Statistics and Probability Letters, 19(3) (1994), 169-176. https://doi.org/10.1016/0167-7152(94)90100-7
  33. Cribari-Neto, F., Vasconcellos, K. L., Nearly unbiased maximum likelihood estimation for the beta distribution, Journal of Statistical Computation and Simulation, 72(2) (2002), 107-118. https://doi.org/10.1080/00949650212144