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Parçacık Sürü Optimizasyon Algoritması Kullanılarak Nakagami Dağılımı için En Çok Olabilirlik Tahmini ve Uygulamaları

Yıl 2023, Cilt: 5 Sayı: 2, 209 - 218, 31.12.2023

Adi Omaia Faouri Pelin Kasap

https://doi.org/10.47112/neufmbd.2023.19

Öz

Nakagami dağılımı, radyo sinyallerinin sönümlenmesini modellemek için ortaya çıkmıştır ve çeşitli disiplinlerde yaygın olarak kullanılmaktadır. Bu çalışmada, dağılımın şekil ve ölçek parametrelerini tahmin etmek için en çok olabilirlik (ML) tahmin yöntemi kullanılmıştır. Ancak, bu dağılım için olabilirlik denklemlerinin açık çözümleri bulunmamaktadır. Bu nedenle, bu denklemlerin çözümü için, parçacık sürüsü optimizasyon (PSO), genetik algoritma (GA) ve quasi-newton (QN) algoritmaları olmak üzere üç temel algoritma kullanılmıştır. Bu algoritmaların performanslarının karşılaştırmaları, yan, hata kareler ortalaması (MSE) ve eksiklik (DEF) kriterleri dikkate alınarak, kapsamlı bir Monte-Carlo simülasyon çalışması ile yapılmıştır. Model, kullanışlılığını göstermek amacıyla dört gerçek veri setine uygulanmıştır.

Anahtar Kelimeler

En çok olabilirlik Nakagami dağılımı Parçacık sürü optimizasyon

Kaynakça

  • M. Nakagami, The m-distribution—A general formula of intensity distribution of rapid fading, Statistical Methods in Radio Wave Propagation, Pergamon. (1960), 3-36. doi: 10.1016/b978-0-08-009306-2.50005-4
  • R.V. Ostrovityanov, F.A. Basalov, The Statistical Theory of Radar Extended Targets. Radio and Communication, Moscow, 1982.
  • W.C. Lee, Mobile Cellular Telecommunications Systems. McGraw-Hill, Inc, New York, 1990.
  • D. Drajic, Introduction to statistical theory of telecommunications. Academic Science, Belgrade, Serbia, 2006.
  • S. Sarkar, N.K. Goel, B.S. Mathur, Adequacy of Nakagami-m distribution function to derive GIUH. Journal of Hydrologic Engineering, 14(10) (2009), 1070-1079. doi: 10.1061/(ASCE)HE.1943-5584.0000103
  • S. Sarkar, N.K. Goel, B.S. Mathur, Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization approach. Journal of Hydrologic Engineering. 15(8) (2010), 658-666. doi: 10.1061/(asce)he.1943-5584.
  • A. Oyetunde, On the introduction of location parameter to Nakagami-m distribution. International Journal of Statistics and Applied Mathematics. 3(4) (2018), 147-154
  • D. Ozonur, H.T.K. Akdur, H. Bayrak, Optimal asymptotic tests for Nakagami distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 22 (2018), 487-492. doi:10.19113/sdufbed.32458
  • P.M. Shankar, C.W. Piccoli, J.M. Reid, F. Forsberg, B.B. Goldberg, Application of the compound probability density function for characterization of breast masses in ultrasound B scans. Physics in Medicine & Biology,. 50(10) (2005), 2241. P.H. Tsui, C.C. Huang, S.H. Wang, Use of Nakagami distribution and logarithmic compression in ultrasonic tissue characterization. Journal of Medical and Biological Engineering. 26(2) (2006), 69-73.
  • J. Cheng, N.C. Beaulieu, Generalized moment estimators for the Nakagami fading parameter. IEEE Communications Letters. 6(4) (2002), 144-146.
  • J. Cheng, N.C. Beaulieu, Maximum-likelihood based estimation of the Nakagami m parameter. IEEE Communications Letters. 5(3) (2001), 101-103.
  • V.M. Artyushenko, V.I. Volovach, Nakagami distribution parameters comparatively estimated by the moment and maximum likelihood methods. Optoelectronics, Instrumentation and Data Processing. 55 (2019), 237-242.
  • J. Schwartz, R.T. Godwin, D.E. Giles, Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution. Journal of Statistical Computation and Simulation. 83(3) (2013), 434-445.
  • A. Abdi, M. Kaveh, Performance comparison of three different estimators for the Nakagami m parameter using Monte Carlo simulation. IEEE communications Letters. 4(4) (2000), 119-121.
  • K. Ahmad, S.P. Ahmad, A. Ahmed, Classical and Bayesian approach in estimation of scale parameter of Nakagami distribution. Journal of Probability and Statistics. 2016.
  • H.Stefanovic, A. Savic, Some general characteristics of Nakagami-m distribution. In 1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011). Tirana, 2011, 695-705.
  • F. Bartolucci, L. Scrucca, Point estimation methods with applications to item response theory models. In International Encyclopedia of Education. 3rd edition Oxford: Elsevier, 2010, 366-373. doi: 10.1016/B978-0-08-044894-7.01376-2
  • D.K. Pratihar, Traditional vs non-traditional optimization tools. In: Basu K (ed) Computational Optimization and Applications, Narosa Publishing House Pvt. Ltd, New Delhi, 2012, 25-33.
  • P. Sreenivas, K. Vijaya, A review on non-traditional optimization algorithm for simultaneous scheduling problems. Journal of Mechanical and Civil Engineering. 12(2) (2015), 50-53. doi:10.9790/1684-12225053
  • J. Kennedy, R. Eberhart, Particle swarm optimization. In Proceedings of ICNN'95-international conference on neural networks, 4, 1995, 1942-1948. IEEE.
  • C. Ren, N. An, J. Wang, L. Li, B. Hu, D. Shang, Optimal parameters selection for BP neural network based on particle swarm optimization: A case study of wind speed forecasting. Knowledge-based Systems. 56 (2014), 226-239. doi: 10.1016/j.knosys.2013.11.015
  • M.H. Ab Talib, I.Z. Mat Darus, Intelligent fuzzy logic with firefly algorithm and particle swarm optimization for semi-active suspension system using magneto-rheological damper. Journal of Vibration and Control. 23(3) (2017), 501-514. doi: 10.1177/1077546315580693
  • S.F.A.X. Júnior, É.F.M. Xavier, J. da Silva Jale, T.A. de Oliveira, A.L.C. Sabino, An application of Particle Swarm Optimization (PSO) algorithm with daily precipitation data in Campina Grande, Paraíba, Brazil. Research, Society and Development. 9(8) (2020), e444985841-e444985841. doi:10.33448/rsd-v9i8.5841
  • J.H. Holland, Adaptation in Natural and Artificial System: an Introduction with Application to Biology, Control, and Artificial Intelligence, University of Michigan Press, Ann Arbor, 1975.
  • D.E. Goldberg, Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley, 1989.
  • W.C. Davidon, Variable metric method for minimization. SIAM Journal on Optimization. 1(1) (1991), 1-17. doi:10.1137/0801001
  • J.M. Martınez, Practical quasi-Newton methods for solving nonlinear systems. Journal of computational and Applied Mathematics. 124(1-2) (2000), 97-121. doi:10.1016/S0377-0427(00)00434-9
  • C.G. Broyden, Quasi-Newton methods and their application to function minimisation. Mathematics of Computation. 21(99) (1967), 368-381.
  • R. Fletcher, M.J. Powell, A rapidly convergent descent method for minimization. The Computer Journal. 6(2) (1963), 163-168.
  • J.C. Gilbert, C. Lemaréchal, Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming. 45(1) (1989), 407-435.
  • C.G. Broyden, The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA Journal of Applied Mathematics. 6(1) (1970), 76-90.
  • R. Fletcher, R. A new approach to variable metric algorithms. The Computer Journal. 13(3) (1970), 317-322.
  • D. Goldfarb, A family of variable-metric methods derived by variational means. Mathematics of Computation. 24(109) (1970), 23-26.
  • D.R. Anderson, K.P. Burnham, G.C. White, Comparison of Akaike information criterion and consistent Akaike information criterion for model selection and statistical inference from capture-recapture studies. Journal of Applied Statistics. 25(2) (1998), 263-282. doi: 10.1080/02664769823250
  • V. Choulakian, M.A. Stephens, Goodness-of-fit tests for the generalized Pareto distribution. Technometrics. 43(4) (2001), 478-484.
  • A. Akinsete, F. Famoye, C. Lee, The beta-Pareto distribution. Statistics. 42(6) (2008), 547–563. doi:10.1080/02331880801983876
  • M.G. Bader, A.M. Priest, Statistical aspects of fibre and bundle strength in hybrid composites. Progress in Science and Engineering of Composites. (1982), 1129-1136.
  • M.W.A. Ramos, P.R.D. Marinho, R.V. da Silva, G.M. Cordeiro, The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics. 34(2) (2013), 107.
  • R.L. Smith, J. Naylor, A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Journal of the Royal Statistical Society Series C: Applied Statistics. 36(3) (1987), 358-369.

Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications

Yıl 2023, Cilt: 5 Sayı: 2, 209 - 218, 31.12.2023

Adi Omaia Faouri Pelin Kasap

https://doi.org/10.47112/neufmbd.2023.19

Öz

The Nakagami distribution originated to model the fading of radio signals and is widely used in various disciplines. In this study, the maximum likelihood (ML) estimation method is used to estimate the shape and scale parameters of the distribution. However, there are no explicit solutions to the likelihood equations for this distribution. Therefore, three main algorithms, the particle swarm optimization algorithm (PSO), the genetic algorithm (GA), and the quasi-newton (QN) algorithm, have been used to solve these equations. Comparisons of the performances of these algorithms have been made with a comprehensive Monte-Carlo simulation study, taking into account the bias, mean squared error (MSE), and deficiency (DEF) criteria. The model has been applied to four real data sets in order to demonstrate its usefulness.

Anahtar Kelimeler

Maximum Likelihood Nakagami Distribution Particle swarm optimization Monte-Carlo simulation

Kaynakça

  • M. Nakagami, The m-distribution—A general formula of intensity distribution of rapid fading, Statistical Methods in Radio Wave Propagation, Pergamon. (1960), 3-36. doi: 10.1016/b978-0-08-009306-2.50005-4
  • R.V. Ostrovityanov, F.A. Basalov, The Statistical Theory of Radar Extended Targets. Radio and Communication, Moscow, 1982.
  • W.C. Lee, Mobile Cellular Telecommunications Systems. McGraw-Hill, Inc, New York, 1990.
  • D. Drajic, Introduction to statistical theory of telecommunications. Academic Science, Belgrade, Serbia, 2006.
  • S. Sarkar, N.K. Goel, B.S. Mathur, Adequacy of Nakagami-m distribution function to derive GIUH. Journal of Hydrologic Engineering, 14(10) (2009), 1070-1079. doi: 10.1061/(ASCE)HE.1943-5584.0000103
  • S. Sarkar, N.K. Goel, B.S. Mathur, Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization approach. Journal of Hydrologic Engineering. 15(8) (2010), 658-666. doi: 10.1061/(asce)he.1943-5584.
  • A. Oyetunde, On the introduction of location parameter to Nakagami-m distribution. International Journal of Statistics and Applied Mathematics. 3(4) (2018), 147-154
  • D. Ozonur, H.T.K. Akdur, H. Bayrak, Optimal asymptotic tests for Nakagami distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 22 (2018), 487-492. doi:10.19113/sdufbed.32458
  • P.M. Shankar, C.W. Piccoli, J.M. Reid, F. Forsberg, B.B. Goldberg, Application of the compound probability density function for characterization of breast masses in ultrasound B scans. Physics in Medicine & Biology,. 50(10) (2005), 2241. P.H. Tsui, C.C. Huang, S.H. Wang, Use of Nakagami distribution and logarithmic compression in ultrasonic tissue characterization. Journal of Medical and Biological Engineering. 26(2) (2006), 69-73.
  • J. Cheng, N.C. Beaulieu, Generalized moment estimators for the Nakagami fading parameter. IEEE Communications Letters. 6(4) (2002), 144-146.
  • J. Cheng, N.C. Beaulieu, Maximum-likelihood based estimation of the Nakagami m parameter. IEEE Communications Letters. 5(3) (2001), 101-103.
  • V.M. Artyushenko, V.I. Volovach, Nakagami distribution parameters comparatively estimated by the moment and maximum likelihood methods. Optoelectronics, Instrumentation and Data Processing. 55 (2019), 237-242.
  • J. Schwartz, R.T. Godwin, D.E. Giles, Improved maximum-likelihood estimation of the shape parameter in the Nakagami distribution. Journal of Statistical Computation and Simulation. 83(3) (2013), 434-445.
  • A. Abdi, M. Kaveh, Performance comparison of three different estimators for the Nakagami m parameter using Monte Carlo simulation. IEEE communications Letters. 4(4) (2000), 119-121.
  • K. Ahmad, S.P. Ahmad, A. Ahmed, Classical and Bayesian approach in estimation of scale parameter of Nakagami distribution. Journal of Probability and Statistics. 2016.
  • H.Stefanovic, A. Savic, Some general characteristics of Nakagami-m distribution. In 1st International Symposium on Computing in Informatics and Mathematics (ISCIM 2011). Tirana, 2011, 695-705.
  • F. Bartolucci, L. Scrucca, Point estimation methods with applications to item response theory models. In International Encyclopedia of Education. 3rd edition Oxford: Elsevier, 2010, 366-373. doi: 10.1016/B978-0-08-044894-7.01376-2
  • D.K. Pratihar, Traditional vs non-traditional optimization tools. In: Basu K (ed) Computational Optimization and Applications, Narosa Publishing House Pvt. Ltd, New Delhi, 2012, 25-33.
  • P. Sreenivas, K. Vijaya, A review on non-traditional optimization algorithm for simultaneous scheduling problems. Journal of Mechanical and Civil Engineering. 12(2) (2015), 50-53. doi:10.9790/1684-12225053
  • J. Kennedy, R. Eberhart, Particle swarm optimization. In Proceedings of ICNN'95-international conference on neural networks, 4, 1995, 1942-1948. IEEE.
  • C. Ren, N. An, J. Wang, L. Li, B. Hu, D. Shang, Optimal parameters selection for BP neural network based on particle swarm optimization: A case study of wind speed forecasting. Knowledge-based Systems. 56 (2014), 226-239. doi: 10.1016/j.knosys.2013.11.015
  • M.H. Ab Talib, I.Z. Mat Darus, Intelligent fuzzy logic with firefly algorithm and particle swarm optimization for semi-active suspension system using magneto-rheological damper. Journal of Vibration and Control. 23(3) (2017), 501-514. doi: 10.1177/1077546315580693
  • S.F.A.X. Júnior, É.F.M. Xavier, J. da Silva Jale, T.A. de Oliveira, A.L.C. Sabino, An application of Particle Swarm Optimization (PSO) algorithm with daily precipitation data in Campina Grande, Paraíba, Brazil. Research, Society and Development. 9(8) (2020), e444985841-e444985841. doi:10.33448/rsd-v9i8.5841
  • J.H. Holland, Adaptation in Natural and Artificial System: an Introduction with Application to Biology, Control, and Artificial Intelligence, University of Michigan Press, Ann Arbor, 1975.
  • D.E. Goldberg, Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley, 1989.
  • W.C. Davidon, Variable metric method for minimization. SIAM Journal on Optimization. 1(1) (1991), 1-17. doi:10.1137/0801001
  • J.M. Martınez, Practical quasi-Newton methods for solving nonlinear systems. Journal of computational and Applied Mathematics. 124(1-2) (2000), 97-121. doi:10.1016/S0377-0427(00)00434-9
  • C.G. Broyden, Quasi-Newton methods and their application to function minimisation. Mathematics of Computation. 21(99) (1967), 368-381.
  • R. Fletcher, M.J. Powell, A rapidly convergent descent method for minimization. The Computer Journal. 6(2) (1963), 163-168.
  • J.C. Gilbert, C. Lemaréchal, Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming. 45(1) (1989), 407-435.
  • C.G. Broyden, The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA Journal of Applied Mathematics. 6(1) (1970), 76-90.
  • R. Fletcher, R. A new approach to variable metric algorithms. The Computer Journal. 13(3) (1970), 317-322.
  • D. Goldfarb, A family of variable-metric methods derived by variational means. Mathematics of Computation. 24(109) (1970), 23-26.
  • D.R. Anderson, K.P. Burnham, G.C. White, Comparison of Akaike information criterion and consistent Akaike information criterion for model selection and statistical inference from capture-recapture studies. Journal of Applied Statistics. 25(2) (1998), 263-282. doi: 10.1080/02664769823250
  • V. Choulakian, M.A. Stephens, Goodness-of-fit tests for the generalized Pareto distribution. Technometrics. 43(4) (2001), 478-484.
  • A. Akinsete, F. Famoye, C. Lee, The beta-Pareto distribution. Statistics. 42(6) (2008), 547–563. doi:10.1080/02331880801983876
  • M.G. Bader, A.M. Priest, Statistical aspects of fibre and bundle strength in hybrid composites. Progress in Science and Engineering of Composites. (1982), 1129-1136.
  • M.W.A. Ramos, P.R.D. Marinho, R.V. da Silva, G.M. Cordeiro, The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics. 34(2) (2013), 107.
  • R.L. Smith, J. Naylor, A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Journal of the Royal Statistical Society Series C: Applied Statistics. 36(3) (1987), 358-369.
Toplam 39 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Hesaplamalı İstatistik, İstatistiksel Analiz, Uygulamalı İstatistik
Bölüm Makaleler
Yazarlar

Adi Omaia Faouri 0000-0003-4499-1240

Pelin Kasap 0000-0002-1106-710X

Erken Görünüm Tarihi 23 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Kabul Tarihi 12 Ekim 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 5 Sayı: 2

Kaynak Göster

APA Faouri, A. O., & Kasap, P. (2023). Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 5(2), 209-218. https://doi.org/10.47112/neufmbd.2023.19
AMA Faouri AO, Kasap P. Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications. NEU Fen Muh Bil Der. Aralık 2023;5(2):209-218. doi:10.47112/neufmbd.2023.19
Chicago Faouri, Adi Omaia, ve Pelin Kasap. “Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm With Applications”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 5, sy. 2 (Aralık 2023): 209-18. https://doi.org/10.47112/neufmbd.2023.19.
EndNote Faouri AO, Kasap P (01 Aralık 2023) Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5 2 209–218.
IEEE A. O. Faouri ve P. Kasap, “Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications”, NEU Fen Muh Bil Der, c. 5, sy. 2, ss. 209–218, 2023, doi: 10.47112/neufmbd.2023.19.
ISNAD Faouri, Adi Omaia - Kasap, Pelin. “Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm With Applications”. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5/2 (Aralık 2023), 209-218. https://doi.org/10.47112/neufmbd.2023.19.
JAMA Faouri AO, Kasap P. Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications. NEU Fen Muh Bil Der. 2023;5:209–218.
MLA Faouri, Adi Omaia ve Pelin Kasap. “Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm With Applications”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 5, sy. 2, 2023, ss. 209-18, doi:10.47112/neufmbd.2023.19.
Vancouver Faouri AO, Kasap P. Maximum Likelihood Estimation for the Nakagami Distribution Using Particle Swarm Optimization Algorithm with Applications. NEU Fen Muh Bil Der. 2023;5(2):209-18.
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