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Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data

Yıl 2025, Cilt: 54 Sayı: 3, 1128 - 1163, 24.06.2025

Mohd Irfan , Anup Kumar Sharma

https://doi.org/10.15672/hujms.1540349

Öz

The present paper studies parametric inference for the inverse Nakagami-m distribution under a unified progressive hybrid censored sample. Maximum likelihood estimates of the unknown parameters are obtained using the Newton-Raphson method and the expectation-maximization algorithm. Approximate confidence intervals for the parameters are constructed via the variance-covariance matrix. Furthermore, Bayes estimates are investigated under the squared error and LINEX loss functions using gamma prior distributions for the unknown parameters. The Markov chain Monte Carlo approximation approach is employed to obtain the Bayes estimates and derive the highest posterior density credible intervals. The issue of hyperparameter selection is also discussed. In addition to Bayes estimates, maximum a posteriori estimates of the unknown parameters are computed using the Newton-Raphson method. The efficacy of the proposed approach is assessed through a Monte Carlo simulation study. The convergence of the MCMC sample is evaluated using various diagnostic plots. Three optimality criteria are presented to select the most suitable progressive scheme from different sampling plans. Two real-world applications that involve the fracture toughness of silicon nitride ($\text{Si}_3\text{N}_4$) and the active repair times (in hours) for an airborne communication transceiver are used to illustrate the practical utility of the proposed methodology.

Anahtar Kelimeler

Bayesian estimation expectation maximization hybrid censoring Nakagami-m distribution optimality

Kaynakça

  • [1] A. Childs, B. Chandrasekar, N. Balakrishnan, and D. Kundu, Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Ann. Inst. Stat. Math. 55, 319-330, 2003.
  • [2] A.I.E.S. Ibrahim, On Estimation and Prediction for the Kumaraswamy Distribution Based on Progressive Censoring Schemes. (Doctoral dissertation, Zagazig University) 2023.
  • [3] A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B Methodol. 39 (1), 1-22, 1977.
  • [4] B. Chandrasekar, A. Childs and N. Balakrishnan Exact likelihood inference for the exponential distribution under generalized TypeI and TypeII hybrid censoring, Nav. Res. Logist. 51 (7), 994-1004, 2004.
  • [5] B. Epstein, Truncated life tests in the exponential case, Ann. Math. Stat. 555-564, 1954.
  • [6] B. Hasselman and M.B. Hasselman, Package nleqslv, R package version 3 (2), 2018.
  • [7] B. Pradhan and D. Kundu, Inference and optimal censoring schemes for progressively censored BirnbaumSaunders distribution, J. Stat. Plan. Inference 143 (6), 1098-1108, 2013.
  • [8] D. Kundu and A. Joarder, Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal. 50 (10), 2509-2528, 2006.
  • [9] D. Kundu, Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring, Technometrics 50 (2), 144-154, 2008.
  • [10] F. Louzada, P. L. Ramos and D. Nascimento, The inverse Nakagami-m distribution: A novel approach in reliability, IEEE Trans. Reliab. 67 (3), 1030-1042, 2018.
  • [11] H. Panahi, Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness, J. Appl. Stat. 44 (14), 2575-2592, 2017.
  • [12] M. Hashempour, A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations, Math. Slovaca 71 (4), 983-1004, 2021.
  • [13] J. Górny and E. Cramer, Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring, Metrika 81 (2), 173-210, 2018.
  • [14] J. Bent. Statistical properties of the generalized inverse Gaussian distribution (Vol. 9). Springer Science & Business Media, 2008.
  • [15] J. Kim and K. Lee, Estimation of the Weibull distribution under unified progressive hybrid censored data, J. Kor. Data Anal. Soc. 20, 21892199, 2018.
  • [16] K. Lee, H. Sun and Y. Cho, Exact likelihood inference of the exponential parameter under generalized Type II progressive hybrid censoring, J KOREAN STAT SOC. 45 (1), 123-136, 2016.
  • [17] L. Wang, S. Dey and Y.M. Tripathi, Classical and Bayesian inference of the inverse Nakagami distribution based on progressive Type-II censored samples, Mathematics 10 (12), 2137, 2022.
  • [18] M.H. Chen and Q.M. Shao, Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comput. Graph. Stat. 8 (1), 69-92, 1999.
  • [19] M. Irfan and A. K. Sharma, Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data, Int. J. Qual. Reliab. Manag. 41 (3), 850-878, 2023.
  • [20] G. S., Mohammad, A new mixture of exponential and Weibull distributions: properties, estimation and relibilty modelling, São Paulo J. Math. Sci. 18 (1), 438-458, 2024.
  • [21] M. Abramowitz and I. A. Stegun, (Eds.), Handbook of mathematical functions with formulas, graphs, and mathematical tables (Vol. 55). US Government printing office, 1968.
  • [22] M. Nakagami, The m-distributionA general formula of intensity distribution of rapid fading, In Statistical methods in radio wave propagation, 3-36, 1960. Pergamon.
  • [23] M. Nassar and A. Elshahhat, Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored Weibull distribution, J. Appl. Stat. 1-25, 2023.
  • [24] M. Plummer, N. Best, K. Cowles and K. Vines, CODA: convergence diagnosis and output analysis for MCMC, R news, 6 (1), 7-11, 2006.
  • [25] M.H. Chen, Q.M. Shao and J.G. Ibrahim, Monte Carlo methods in Bayesian computation, Springer Science & Business Media, 2012.
  • [26] N. Balakrishnan and R. Aggarwala, Progressive censoring: theory, methods, and applications, Springer Science & Business Media, 2000.
  • [27] N. Balakrishnan, A. Rasouli and N. Sanjari Farsipour, Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution, J. Stat. Comput. Simul. 78 (5), 475-488, 2008.
  • [28] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (6), 1087- 1092, 1953.
  • [29] O.E. Abo-Kasem, A.R. El Saeed, and A.I. El Sayed, Optimal sampling and statistical inferences for Kumaraswamy distribution under progressive Type-II censoring schemes, Sci. Rep. 13 (1), 12063, 2023.
  • [30] R.C.H. Cheng and N.A.K. Amin, Estimating parameters in continuous univariate distributions with a shifted origin, J. R. Stat. Soc. Ser. B Methodol. 45 (3), 394-403, 1983.
  • [31] G. Shaheed, Novel Weighted G family of Probability Distributions with Properties, Modelling and Different Methods of Estimation, Stat. Optim. Inf. Comput. 10 (4), 1143-1161, 2022.
  • [32] S.A. Lone, H. Panahi, S. Anwar and S. Shahab, Estimations and optimal censoring schemes for the unified progressive hybrid gamma-mixed Rayleigh distribution, Electron. Res. Arch. 31 (8), 4729-4752, 2023.
  • [33] S. Dey, T. Dey and D.J. Luckett, Statistical inference for the generalized inverted exponential distribution based on upper record values, Math. Comput. Simul. 120, 64-78, 2016.
  • [34] S. Dutta and S. Kayal, Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme, J. Appl. Stat. 51 (1), 1-33, 2024.
  • [35] W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57, 97-109, 1970.

Yıl 2025, Cilt: 54 Sayı: 3, 1128 - 1163, 24.06.2025

Mohd Irfan , Anup Kumar Sharma

https://doi.org/10.15672/hujms.1540349

Öz

Kaynakça

  • [1] A. Childs, B. Chandrasekar, N. Balakrishnan, and D. Kundu, Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Ann. Inst. Stat. Math. 55, 319-330, 2003.
  • [2] A.I.E.S. Ibrahim, On Estimation and Prediction for the Kumaraswamy Distribution Based on Progressive Censoring Schemes. (Doctoral dissertation, Zagazig University) 2023.
  • [3] A.P. Dempster, N.M. Laird and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B Methodol. 39 (1), 1-22, 1977.
  • [4] B. Chandrasekar, A. Childs and N. Balakrishnan Exact likelihood inference for the exponential distribution under generalized TypeI and TypeII hybrid censoring, Nav. Res. Logist. 51 (7), 994-1004, 2004.
  • [5] B. Epstein, Truncated life tests in the exponential case, Ann. Math. Stat. 555-564, 1954.
  • [6] B. Hasselman and M.B. Hasselman, Package nleqslv, R package version 3 (2), 2018.
  • [7] B. Pradhan and D. Kundu, Inference and optimal censoring schemes for progressively censored BirnbaumSaunders distribution, J. Stat. Plan. Inference 143 (6), 1098-1108, 2013.
  • [8] D. Kundu and A. Joarder, Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal. 50 (10), 2509-2528, 2006.
  • [9] D. Kundu, Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring, Technometrics 50 (2), 144-154, 2008.
  • [10] F. Louzada, P. L. Ramos and D. Nascimento, The inverse Nakagami-m distribution: A novel approach in reliability, IEEE Trans. Reliab. 67 (3), 1030-1042, 2018.
  • [11] H. Panahi, Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness, J. Appl. Stat. 44 (14), 2575-2592, 2017.
  • [12] M. Hashempour, A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations, Math. Slovaca 71 (4), 983-1004, 2021.
  • [13] J. Górny and E. Cramer, Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring, Metrika 81 (2), 173-210, 2018.
  • [14] J. Bent. Statistical properties of the generalized inverse Gaussian distribution (Vol. 9). Springer Science & Business Media, 2008.
  • [15] J. Kim and K. Lee, Estimation of the Weibull distribution under unified progressive hybrid censored data, J. Kor. Data Anal. Soc. 20, 21892199, 2018.
  • [16] K. Lee, H. Sun and Y. Cho, Exact likelihood inference of the exponential parameter under generalized Type II progressive hybrid censoring, J KOREAN STAT SOC. 45 (1), 123-136, 2016.
  • [17] L. Wang, S. Dey and Y.M. Tripathi, Classical and Bayesian inference of the inverse Nakagami distribution based on progressive Type-II censored samples, Mathematics 10 (12), 2137, 2022.
  • [18] M.H. Chen and Q.M. Shao, Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comput. Graph. Stat. 8 (1), 69-92, 1999.
  • [19] M. Irfan and A. K. Sharma, Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data, Int. J. Qual. Reliab. Manag. 41 (3), 850-878, 2023.
  • [20] G. S., Mohammad, A new mixture of exponential and Weibull distributions: properties, estimation and relibilty modelling, São Paulo J. Math. Sci. 18 (1), 438-458, 2024.
  • [21] M. Abramowitz and I. A. Stegun, (Eds.), Handbook of mathematical functions with formulas, graphs, and mathematical tables (Vol. 55). US Government printing office, 1968.
  • [22] M. Nakagami, The m-distributionA general formula of intensity distribution of rapid fading, In Statistical methods in radio wave propagation, 3-36, 1960. Pergamon.
  • [23] M. Nassar and A. Elshahhat, Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored Weibull distribution, J. Appl. Stat. 1-25, 2023.
  • [24] M. Plummer, N. Best, K. Cowles and K. Vines, CODA: convergence diagnosis and output analysis for MCMC, R news, 6 (1), 7-11, 2006.
  • [25] M.H. Chen, Q.M. Shao and J.G. Ibrahim, Monte Carlo methods in Bayesian computation, Springer Science & Business Media, 2012.
  • [26] N. Balakrishnan and R. Aggarwala, Progressive censoring: theory, methods, and applications, Springer Science & Business Media, 2000.
  • [27] N. Balakrishnan, A. Rasouli and N. Sanjari Farsipour, Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution, J. Stat. Comput. Simul. 78 (5), 475-488, 2008.
  • [28] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (6), 1087- 1092, 1953.
  • [29] O.E. Abo-Kasem, A.R. El Saeed, and A.I. El Sayed, Optimal sampling and statistical inferences for Kumaraswamy distribution under progressive Type-II censoring schemes, Sci. Rep. 13 (1), 12063, 2023.
  • [30] R.C.H. Cheng and N.A.K. Amin, Estimating parameters in continuous univariate distributions with a shifted origin, J. R. Stat. Soc. Ser. B Methodol. 45 (3), 394-403, 1983.
  • [31] G. Shaheed, Novel Weighted G family of Probability Distributions with Properties, Modelling and Different Methods of Estimation, Stat. Optim. Inf. Comput. 10 (4), 1143-1161, 2022.
  • [32] S.A. Lone, H. Panahi, S. Anwar and S. Shahab, Estimations and optimal censoring schemes for the unified progressive hybrid gamma-mixed Rayleigh distribution, Electron. Res. Arch. 31 (8), 4729-4752, 2023.
  • [33] S. Dey, T. Dey and D.J. Luckett, Statistical inference for the generalized inverted exponential distribution based on upper record values, Math. Comput. Simul. 120, 64-78, 2016.
  • [34] S. Dutta and S. Kayal, Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme, J. Appl. Stat. 51 (1), 1-33, 2024.
  • [35] W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57, 97-109, 1970.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

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

Mohd Irfan 0009-0000-2791-1005

Anup Kumar Sharma 0000-0002-3958-1901

Erken Görünüm Tarihi 28 Mayıs 2025
Yayımlanma Tarihi 24 Haziran 2025
Gönderilme Tarihi 29 Ağustos 2024
Kabul Tarihi 9 Mayıs 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 54 Sayı: 3

Kaynak Göster

APA Irfan, M., & Sharma, A. K. (2025). Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data. Hacettepe Journal of Mathematics and Statistics, 54(3), 1128-1163. https://doi.org/10.15672/hujms.1540349
AMA Irfan M, Sharma AK. Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data. Hacettepe Journal of Mathematics and Statistics. Haziran 2025;54(3):1128-1163. doi:10.15672/hujms.1540349
Chicago Irfan, Mohd, ve Anup Kumar Sharma. “Optimal Plan and Statistical Inference for the Inverse Nakagami-M Distribution Based on Unified Progressive Hybrid Censored Data”. Hacettepe Journal of Mathematics and Statistics 54, sy. 3 (Haziran 2025): 1128-63. https://doi.org/10.15672/hujms.1540349.
EndNote Irfan M, Sharma AK (01 Haziran 2025) Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data. Hacettepe Journal of Mathematics and Statistics 54 3 1128–1163.
IEEE M. Irfan ve A. K. Sharma, “Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data”, Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 3, ss. 1128–1163, 2025, doi: 10.15672/hujms.1540349.
ISNAD Irfan, Mohd - Sharma, Anup Kumar. “Optimal Plan and Statistical Inference for the Inverse Nakagami-M Distribution Based on Unified Progressive Hybrid Censored Data”. Hacettepe Journal of Mathematics and Statistics 54/3 (Haziran 2025), 1128-1163. https://doi.org/10.15672/hujms.1540349.
JAMA Irfan M, Sharma AK. Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data. Hacettepe Journal of Mathematics and Statistics. 2025;54:1128–1163.
MLA Irfan, Mohd ve Anup Kumar Sharma. “Optimal Plan and Statistical Inference for the Inverse Nakagami-M Distribution Based on Unified Progressive Hybrid Censored Data”. Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 3, 2025, ss. 1128-63, doi:10.15672/hujms.1540349.
Vancouver Irfan M, Sharma AK. Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data. Hacettepe Journal of Mathematics and Statistics. 2025;54(3):1128-63.

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