Research Article
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Year 2023, Volume: 44 Issue: 1, 229 - 235, 26.03.2023
https://doi.org/10.17776/csj.1122736

Abstract

References

  • [1] Shankar P.M., Ultrasonic tissue characterization using a generalized Nakagami model, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 48 (6) (2001) 1716-1720.
  • [2] Stacy E.W., A generalization of the gamma distribution, Ann. Math. Stat., 33 (3) (1962) 1187-1192.
  • [3] Nakagami M., The m-distribution: a general formulation of intensity distribution of rapid fading, Statistical Method in Radio Wave Propagation, W.C. Hoffman (ed.), Pergamon, (1960) 3–36.
  • [4] Ibnkahla M., Signal Processing for Mobile Communications, CRC Press, Washington, (2004).
  • [5] Nakahara H., Carcolé E., Maximum-likelihood method for estimating coda Q and the Nakagami-m parameter, Bulletin of the Seismological Society of America, 100 (6) (2010) 3174-3182.
  • [6] Sarkar S., Goel N.K., Mathur B.S., Adequacy of Nakagami-m distribution function to derive GIUH, J. Hydrol. Eng., 14 (10) (2009) 1070-1079.
  • [7] Sarkar S., Goel N.K., Mathur B.S., Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization approach, J. Hydrol. Eng., 15 (8) (2010) 658-666.
  • [8] Datta P., Gupta A., Agrawal R., Statistical modeling of B-Mode clinical kidney images, Medical Imaging, m-Health and Emerging Communication Systems (MedCom), Greater Noida, (2014) 222-229.
  • [9] Alavi O., Mohammadi K., Mostafaeipour A., Evaluating the suitability of wind speed probability distribution models: A case of study of east and southeast parts of Iran, Energy Convers. Manage., 119 (2016) 101-108.
  • [10] Ahmad K., Ahmad S.P., Ahmed A., Classical and Bayesian approach in estimation of scale parameter of Nakagami distribution, J. Probab. Stat., (2016) 2016.
  • [11] Ramos P.L., Louzada F., Ramos E., An Efficient, Closed-Form MAP Estimator for Nakagami-m Fading Parameter, IEEE Commun. Lett., 20 (11) (2016) 2328-2331.
  • [12] Ramos P.L., Louzada, F., Ramos, E., Posterior Properties of the Nakagami-m Distribution Using Noninformative Priors and Applications in Reliability, IEEE Trans. Reliab., 67 (1) (2017) 105-117.
  • [13] Kumar K., Garg, R., Krishna, H., Nakagami distribution as a reliability model under progressive censoring, Int. J. Syst. Assur. Eng. Manag., 8 (1) (2017) 109-122.
  • [14] Ozonur D., Akdur, H.T.K., Bayrak, H., Optimal Asymptotic Tests for Nakagami Distribution, SDU J. Nat. Appl. Sci., 22 (2018) 487-492.
  • [15] Ozonur D., Paul, S., Goodness of fit tests of the two-parameter gamma distribution against the three-parameter generalized gamma distribution, Commun. Stat.-Simul. Comput., 51 (3) (2022) 687-697.
  • [16] Rayner, J.C., Thas, O., Best, D.J., Smooth tests of goodness of fit: using R. John Wiley & Sons, Singapore, (2009).
  • [17] Bera A.K., Bilias Y., Rao's score, Neyman's C (α) and Silvey's LM tests: an essay on historical developments and some new results, J. Stat. Plann. Inference, 97 (1) (2001) 9-44.
  • [18] Balakrishnan N., Kannan N., Nagaraja H.N., Advances in ranking and selection, multiple comparisons, and reliability: methodology and applications, Birkhauser, Boston, (2005).
  • [19] Rao C.R., Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation, Proceedings of Cambridge Philosophical Society, 44 (1948) 50-57.
  • [20]Neyman J., Optimal asymptotic tests of composite statistical hypotheses, Probability and statistics, Wiley, New York (1959).
  • [21] Bartlett M.S., Approximate confidence intervals, Biometrika, 40 (1/2) (1953) 12-19.
  • [22] Abdi A., Kaveh M., Performance comparison of three different estimators for the Nakagami m parameter using Monte Carlo simulation, IEEE Commun. Lett., 4 (4) (2000) 119-121.
  • [23]Cheng J., Beaulieu N.C., Generalized moment estimators for the Nakagami fading parameter, IEEE Commun. Lett., 6 (4) (2002) 144-146.
  • [24]Moran P.A., On asymptotically optimal tests of composite hypotheses, Biometrika, 57 (1) (1970) 47-55.
  • [25]Cox D.R., Hinkley D.V., Theoretical Statistics, Chapman & Hall, London, (1974).
  • [26]Tilbi D., Seddik-Ameur N., Chi-squared goodness-of-fit tests for the generalized Rayleigh distribution, J. Stat. Theory Pract., 11 (4) (2017) 594-603.
  • [27] Lee E.T., Wang J., Statistical methods for survival data analysis, Vol. 476, John Wiley & Sons, (2003).

Evaluating the Goodness of Fit of Generalized Nakagami Distribution

Year 2023, Volume: 44 Issue: 1, 229 - 235, 26.03.2023
https://doi.org/10.17776/csj.1122736

Abstract

The Generalized Nakagami distribution is a popular distribution in wireless communication. This distribution includes the Nakagami distribution as a special case. Likelihood ratio, score, and two C(α) tests are developed to evaluate the fit of Nakagami distribution against Generalized Nakagami distribution. A Monte Carlo simulation study is performed in order to investigate the performance of these tests with regard to Type I errors and powers of tests. Finally, two data sets are analyzed using the proposed goodness of fit tests.

References

  • [1] Shankar P.M., Ultrasonic tissue characterization using a generalized Nakagami model, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 48 (6) (2001) 1716-1720.
  • [2] Stacy E.W., A generalization of the gamma distribution, Ann. Math. Stat., 33 (3) (1962) 1187-1192.
  • [3] Nakagami M., The m-distribution: a general formulation of intensity distribution of rapid fading, Statistical Method in Radio Wave Propagation, W.C. Hoffman (ed.), Pergamon, (1960) 3–36.
  • [4] Ibnkahla M., Signal Processing for Mobile Communications, CRC Press, Washington, (2004).
  • [5] Nakahara H., Carcolé E., Maximum-likelihood method for estimating coda Q and the Nakagami-m parameter, Bulletin of the Seismological Society of America, 100 (6) (2010) 3174-3182.
  • [6] Sarkar S., Goel N.K., Mathur B.S., Adequacy of Nakagami-m distribution function to derive GIUH, J. Hydrol. Eng., 14 (10) (2009) 1070-1079.
  • [7] Sarkar S., Goel N.K., Mathur B.S., Performance investigation of Nakagami-m distribution to derive flood hydrograph by genetic algorithm optimization approach, J. Hydrol. Eng., 15 (8) (2010) 658-666.
  • [8] Datta P., Gupta A., Agrawal R., Statistical modeling of B-Mode clinical kidney images, Medical Imaging, m-Health and Emerging Communication Systems (MedCom), Greater Noida, (2014) 222-229.
  • [9] Alavi O., Mohammadi K., Mostafaeipour A., Evaluating the suitability of wind speed probability distribution models: A case of study of east and southeast parts of Iran, Energy Convers. Manage., 119 (2016) 101-108.
  • [10] Ahmad K., Ahmad S.P., Ahmed A., Classical and Bayesian approach in estimation of scale parameter of Nakagami distribution, J. Probab. Stat., (2016) 2016.
  • [11] Ramos P.L., Louzada F., Ramos E., An Efficient, Closed-Form MAP Estimator for Nakagami-m Fading Parameter, IEEE Commun. Lett., 20 (11) (2016) 2328-2331.
  • [12] Ramos P.L., Louzada, F., Ramos, E., Posterior Properties of the Nakagami-m Distribution Using Noninformative Priors and Applications in Reliability, IEEE Trans. Reliab., 67 (1) (2017) 105-117.
  • [13] Kumar K., Garg, R., Krishna, H., Nakagami distribution as a reliability model under progressive censoring, Int. J. Syst. Assur. Eng. Manag., 8 (1) (2017) 109-122.
  • [14] Ozonur D., Akdur, H.T.K., Bayrak, H., Optimal Asymptotic Tests for Nakagami Distribution, SDU J. Nat. Appl. Sci., 22 (2018) 487-492.
  • [15] Ozonur D., Paul, S., Goodness of fit tests of the two-parameter gamma distribution against the three-parameter generalized gamma distribution, Commun. Stat.-Simul. Comput., 51 (3) (2022) 687-697.
  • [16] Rayner, J.C., Thas, O., Best, D.J., Smooth tests of goodness of fit: using R. John Wiley & Sons, Singapore, (2009).
  • [17] Bera A.K., Bilias Y., Rao's score, Neyman's C (α) and Silvey's LM tests: an essay on historical developments and some new results, J. Stat. Plann. Inference, 97 (1) (2001) 9-44.
  • [18] Balakrishnan N., Kannan N., Nagaraja H.N., Advances in ranking and selection, multiple comparisons, and reliability: methodology and applications, Birkhauser, Boston, (2005).
  • [19] Rao C.R., Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation, Proceedings of Cambridge Philosophical Society, 44 (1948) 50-57.
  • [20]Neyman J., Optimal asymptotic tests of composite statistical hypotheses, Probability and statistics, Wiley, New York (1959).
  • [21] Bartlett M.S., Approximate confidence intervals, Biometrika, 40 (1/2) (1953) 12-19.
  • [22] Abdi A., Kaveh M., Performance comparison of three different estimators for the Nakagami m parameter using Monte Carlo simulation, IEEE Commun. Lett., 4 (4) (2000) 119-121.
  • [23]Cheng J., Beaulieu N.C., Generalized moment estimators for the Nakagami fading parameter, IEEE Commun. Lett., 6 (4) (2002) 144-146.
  • [24]Moran P.A., On asymptotically optimal tests of composite hypotheses, Biometrika, 57 (1) (1970) 47-55.
  • [25]Cox D.R., Hinkley D.V., Theoretical Statistics, Chapman & Hall, London, (1974).
  • [26]Tilbi D., Seddik-Ameur N., Chi-squared goodness-of-fit tests for the generalized Rayleigh distribution, J. Stat. Theory Pract., 11 (4) (2017) 594-603.
  • [27] Lee E.T., Wang J., Statistical methods for survival data analysis, Vol. 476, John Wiley & Sons, (2003).
There are 27 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Deniz Özonur 0000-0002-7622-1008

Publication Date March 26, 2023
Submission Date May 28, 2022
Acceptance Date February 27, 2023
Published in Issue Year 2023Volume: 44 Issue: 1

Cite

APA Özonur, D. (2023). Evaluating the Goodness of Fit of Generalized Nakagami Distribution. Cumhuriyet Science Journal, 44(1), 229-235. https://doi.org/10.17776/csj.1122736