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Optimal Asymptotic Tests for Nakagami Distribution

Year 2018, Volume: 22 Issue: Special, 487 - 492, 05.10.2018

Abstract

Nakagami distribution is often used to model positive valued data with right skewness. The distribution includes some familiar distributions as special cases such as Rayleigh and Half-normal distributions. In real life applications, one of the simpler model may be sufficient to describe data. The aim of this paper is to adapt tests of goodness of fit of the Rayleigh distribution against Nakagami distribution. In this study likelihood ratio, and score tests are specifically obtained. These tests are then compared in terms of type I error and power of test by a Monte Carlo simulation study.

References

  • [1] Nakagami, M. 1960. The m-distribution: a general formulation of intensity distribution of rapid fading. In W.C. Hoffman (ed.), Statistical Method in Radio Wave Propagation. Tarrytown, NY: Pergamon, 3–36.
  • [2] Sarkar, S., Goel, N.K., Mathur, B.S. 2009. Adequacy of Nakagami-m distribution function to derive GIUH. J. Hydrol. Eng. 14, 1070–1079.
  • [3] Sarkar, S., Goel, N.K., Mathur, B.S. 2010. Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization approach. J. Hydrol. Eng. 15, 658–666.
  • [4] Shankar, P.M., Piccoli, C.W., Reid, J.M., Forsberg, F., Goldberg, B.B. 2005. Application of the compound probability density function for characterization of breast masses in ultrasound B scans. Phys. Med. Biol. 50, 2241–2248.
  • [5] Tsui, P.H., Huang, C.C.,Wang, S.H. 2006. Use of Nakagami distribution and logarithmic compression in ultrasonic tissue characterization. J. Med. Biol. Eng. 26, 69–73.
  • [6] Kim, K., Latchman, H.A. 2009. Statistical traffic modeling of MPEG frame size: Experiments and analysis. J. Systemics, Cybernetics Inform. 7, 54–59.
  • [7] Carcole, E., Sato, H. 2009. Statistics of the punctuations of the amplitude of coda waves of local earthquakes. Abstracts of the Seismological Society of Japan, Kyoto, Japan, C31–13.
  • [8] Nakahara, H., Carcole, E. 2010. Maximum likelihood method for estimating Coda Q and the Nakagami-m parameter. Bull. Seismol. Soc. Am. 100, 3174-3182.
  • [9] Ozonur, D., Akdur, H.T.K., Bayrak, H. 2017. A comparison of goodness of fit tests of Rayleigh distribution against Nakagami distribution. 10th International Statistics Congress, 06-08 December, Ankara, 107.
  • [10] Rao, C.R. 1947. Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation. Proceedings of Cambridge Philosophical Society 44, 50-57.
  • [11] Moran, P.A. 1970. On asymptotically optimal tests of composite hypotheses. Biometrika, 57(1), 47-55.
  • [12] Cox, D.R, Hinkley, D.V. 1974. Theoretical Statistics. Chapman and Hall: New York, 511p.
  • [13] Bartoo, J.B, Puri, P.S. 1967. On optimal asymptotic tests of composite statistical hypotheses. Annals of Mathematical Statistics, 38, 1845-1852.
  • [14] Breslow, N.E. 1990. Test of hypotheses in over-dispersed Poisson and other quasi-likelihood models. Journal of American Statistical Association, 85, 565-571.
  • [15] Rayner, J.C., Thas, O., Best, D. J. 2009. Smooth tests of goodness of fit: using R. John Wiley & Sons, 272p.
  • [16] Bera, A.K., Bilias, Y. 2001. Rao's score, Neyman's C (α) and Silvey's LM tests: an essay on historical developments and some new results. Journal of Statistical Planning and Inference, 97(1), 9-44.
  • [17] Balakrishnan, N., Kannan, N., Nagaraja, H.N. 2007. Advances in ranking and selection, multiple comparisons, and reliability: methodology and applications. Springer Science & Business Media, 412p.
  • [18] Neyman J. 1959. Optimal asymptotic tests of composite statistical hypotheses. Probability and statistics, 57, 213.
Year 2018, Volume: 22 Issue: Special, 487 - 492, 05.10.2018

Abstract

References

  • [1] Nakagami, M. 1960. The m-distribution: a general formulation of intensity distribution of rapid fading. In W.C. Hoffman (ed.), Statistical Method in Radio Wave Propagation. Tarrytown, NY: Pergamon, 3–36.
  • [2] Sarkar, S., Goel, N.K., Mathur, B.S. 2009. Adequacy of Nakagami-m distribution function to derive GIUH. J. Hydrol. Eng. 14, 1070–1079.
  • [3] Sarkar, S., Goel, N.K., Mathur, B.S. 2010. Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization approach. J. Hydrol. Eng. 15, 658–666.
  • [4] Shankar, P.M., Piccoli, C.W., Reid, J.M., Forsberg, F., Goldberg, B.B. 2005. Application of the compound probability density function for characterization of breast masses in ultrasound B scans. Phys. Med. Biol. 50, 2241–2248.
  • [5] Tsui, P.H., Huang, C.C.,Wang, S.H. 2006. Use of Nakagami distribution and logarithmic compression in ultrasonic tissue characterization. J. Med. Biol. Eng. 26, 69–73.
  • [6] Kim, K., Latchman, H.A. 2009. Statistical traffic modeling of MPEG frame size: Experiments and analysis. J. Systemics, Cybernetics Inform. 7, 54–59.
  • [7] Carcole, E., Sato, H. 2009. Statistics of the punctuations of the amplitude of coda waves of local earthquakes. Abstracts of the Seismological Society of Japan, Kyoto, Japan, C31–13.
  • [8] Nakahara, H., Carcole, E. 2010. Maximum likelihood method for estimating Coda Q and the Nakagami-m parameter. Bull. Seismol. Soc. Am. 100, 3174-3182.
  • [9] Ozonur, D., Akdur, H.T.K., Bayrak, H. 2017. A comparison of goodness of fit tests of Rayleigh distribution against Nakagami distribution. 10th International Statistics Congress, 06-08 December, Ankara, 107.
  • [10] Rao, C.R. 1947. Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation. Proceedings of Cambridge Philosophical Society 44, 50-57.
  • [11] Moran, P.A. 1970. On asymptotically optimal tests of composite hypotheses. Biometrika, 57(1), 47-55.
  • [12] Cox, D.R, Hinkley, D.V. 1974. Theoretical Statistics. Chapman and Hall: New York, 511p.
  • [13] Bartoo, J.B, Puri, P.S. 1967. On optimal asymptotic tests of composite statistical hypotheses. Annals of Mathematical Statistics, 38, 1845-1852.
  • [14] Breslow, N.E. 1990. Test of hypotheses in over-dispersed Poisson and other quasi-likelihood models. Journal of American Statistical Association, 85, 565-571.
  • [15] Rayner, J.C., Thas, O., Best, D. J. 2009. Smooth tests of goodness of fit: using R. John Wiley & Sons, 272p.
  • [16] Bera, A.K., Bilias, Y. 2001. Rao's score, Neyman's C (α) and Silvey's LM tests: an essay on historical developments and some new results. Journal of Statistical Planning and Inference, 97(1), 9-44.
  • [17] Balakrishnan, N., Kannan, N., Nagaraja, H.N. 2007. Advances in ranking and selection, multiple comparisons, and reliability: methodology and applications. Springer Science & Business Media, 412p.
  • [18] Neyman J. 1959. Optimal asymptotic tests of composite statistical hypotheses. Probability and statistics, 57, 213.
There are 18 citations in total.

Details

Journal Section Articles
Authors

Deniz Ozonur

Hatice Tül Kübra Akdur This is me

Hülya Bayrak

Publication Date October 5, 2018
Published in Issue Year 2018 Volume: 22 Issue: Special

Cite

APA Ozonur, D., Akdur, H. T. K., & Bayrak, H. (2018). Optimal Asymptotic Tests for Nakagami Distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22, 487-492.
AMA Ozonur D, Akdur HTK, Bayrak H. Optimal Asymptotic Tests for Nakagami Distribution. SDÜ Fen Bil Enst Der. October 2018;22:487-492.
Chicago Ozonur, Deniz, Hatice Tül Kübra Akdur, and Hülya Bayrak. “Optimal Asymptotic Tests for Nakagami Distribution”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, October (October 2018): 487-92.
EndNote Ozonur D, Akdur HTK, Bayrak H (October 1, 2018) Optimal Asymptotic Tests for Nakagami Distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 487–492.
IEEE D. Ozonur, H. T. K. Akdur, and H. Bayrak, “Optimal Asymptotic Tests for Nakagami Distribution”, SDÜ Fen Bil Enst Der, vol. 22, pp. 487–492, 2018.
ISNAD Ozonur, Deniz et al. “Optimal Asymptotic Tests for Nakagami Distribution”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (October 2018), 487-492.
JAMA Ozonur D, Akdur HTK, Bayrak H. Optimal Asymptotic Tests for Nakagami Distribution. SDÜ Fen Bil Enst Der. 2018;22:487–492.
MLA Ozonur, Deniz et al. “Optimal Asymptotic Tests for Nakagami Distribution”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, 2018, pp. 487-92.
Vancouver Ozonur D, Akdur HTK, Bayrak H. Optimal Asymptotic Tests for Nakagami Distribution. SDÜ Fen Bil Enst Der. 2018;22:487-92.

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