Research Article
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Year 2023, Volume: 44 Issue: 1, 229 - 235, 26.03.2023

Deniz Özonur

https://doi.org/10.17776/csj.1122736
https://izlik.org/JA83AY93CS

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

Deniz Özonur

https://doi.org/10.17776/csj.1122736
https://izlik.org/JA83AY93CS

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.

Keywords

C(α) test Generalized Nakagami distribution Likelihood ratio test Power of test Score test

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 Research Article
Authors

Deniz Özonur 0000-0002-7622-1008

Submission Date May 28, 2022
Acceptance Date February 27, 2023
Publication Date March 26, 2023
DOI https://doi.org/10.17776/csj.1122736
IZ https://izlik.org/JA83AY93CS
Published in Issue Year 2023 Volume: 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

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