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Point Estimation for the Inverse Rayleigh Distribution under Type-II Left and Right Censoring

Year 2025, Volume: 46 Issue: 1, 179 - 184, 25.03.2025

Sümeyra Sert , Coşkun Kuş

https://doi.org/10.17776/csj.1460135

Abstract

The Inverse Rayleigh distribution is frequently utilized in reliability and survival analysis. This study focuses on deriving modified maximum likelihood estimators for the scale parameter of the Inverse Rayleigh distribution under Type-II left and right censoring. The efficacy of the proposed estimators is assessed through comparison with Anderson-Darling, Kolmogorov-Smirnov, and Cramér-von Mises type estimators via Monte Carlo simulations across various censoring schemes and parameter configurations. Additionally, a numerical example is presented to illustrate the proposed methodology. The simulation study demonstrates that the proposed estimators outperform the others. Additionally, given their explicit nature, the proposed estimators can serve as initial values for obtaining the maximum likelihood estimator.

Keywords

Anderson-Darling statistic Cramér-von mises Left and right censoring Kolmogorov-Smirnov statistics Modified maximum likelihood estimation.

References

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  • [2] Hossain M. P., Omar M. H., Riaz M., Arafat S. Y., On designing a new control chart for Rayleigh distributed processes with an application to monitor glass fiber strength, Communications in Statistics-Simulation and Computation, 51(6) (2022) 3168-3184.
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  • [4] Aslam M., Jun C. H., A group acceptance sampling plan for truncated life test having Weibull distribution. Journal of Applied Statistics, 36(9) (2009) 1021-1027.
  • [5] Soliman A., Amin E. A., Abd-El Aziz A. A., Estimation and prediction from inverse Rayleigh distribution based on lower record values, Applied Mathematical Sciences, 4(62) (2010) 3057-3066.
  • [6] Prakash G., Shrinkage Estimation in the Inverse Rayleigh Distribution, Journal of Modern Applied Statistical Methods, 9 (2010) 209-220.
  • [7] Dey S., Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution, Malaysian Journal of Mathematical Sciences, 6(1) (2012) 113-124.
  • [8] Akdoğan Y., Özkan E., Karakaya K., Tanış C., Estimation Of Parameter For Inverse Rayleigh Distribution Under Type-I Hybrid Censored Samples, Sigma Journal of Engineering and Natural Sciences, 38(4) (2020) 1705-1711.
  • [9] Adeoti O. A., Gadde S. R., Moving average control charts for the Rayleigh and inverse Rayleigh distributions under time truncated life test, Quality and Reliability Engineering International, 37(8) (2021) 3552-3567.
  • [10] Athirakrishnan R. B., Abdul-Sathar E. I., E-Bayesian and hierarchical Bayesian estimation of inverse Rayleigh distribution, American Journal of Mathematical and Management Sciences, 41(1) (2022) 70-87.
  • [11] Kumar R., Gupta R., Bayesian analysis of inverse Rayleigh distribution under non-informative prior for different loss functions, Thailand Statistician, 21(1) (2023) 76-92.
  • [12] Karakaya K., Kınacı İ., Akdoğan Y., Saraçoğlu B., Kuş C., Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring, Pakistan Journal of Statistics and Operation Research, (2024) 37-47.
  • [13] Lalitha S., Mishra A., Modified maximum likelihood estimation for Rayleigh distribution, Communications in Statistics-Theory and Methods, 25(2) (1996) 389-401.
  • [14] Wingo D. R., Maximum likelihood estimation of Burr XII distribution parameters under type II censoring, Microelectronics Reliability, 33(9) (1993) 1251-1257.
  • [15] Balakrishnan N., Kundu D., Ng K. T., Kannan N., Point and interval estimation for a simple step-stress model with Type-II censoring, Journal of Quality Technology, 39(1) (2007) 35-47.
  • [16] Jaheen Z. F., Okasha H. M., E-Bayesian estimation for the Burr type XII model based on type-2 censoring, Applied Mathematical Modelling, 35(10) (2011) 4730-4737.
  • [17] Almetwally E. M., Sabry M. A., Alharbi R., Alnagar D., Mubarak S. A., Hafez E. H., Marshall–olkin alpha power Weibull distribution: different methods of estimation based on type-I and type-II censoring, Complexity, (2021) 1-18.
  • [18] Biçer H. D., Öztürker B., Estimation procedures on Type-II censored data from a scaled Muth distribution, Sigma Journal of Engineering and Natural Sciences, 39(2) (2021) 148-158.
  • [19] Schneider H., Weissfeld L. (1986). Inference based on Type II censored samples, Biometrics, 531-536.
  • [20] Balakrishnan N., Aggarwala R., Progressive censoring: theory, methods, and applications, Springer Science & Business Media, (2000).
  • [21] Karakaya K., Tanış C., Different methods of estimation for the one parameter Akash distribution, Cumhuriyet Science Journal, 41(4) (2020a) 944-950.
  • [22] Karakaya K., Tanış C., Estimating the parameters of Xgamma Weibull distribution, Adıyaman University Journal of Science, 10(2) (2020b) 557-571.
  • [23] Tanış C., Karakaya K., On Estimating Parameters of Lindley-Geometric Distribution, Eskişehir Technical University Journal of Science and Technology A-Applied Sciences and Engineering, 22(2) (2021) 160-167.
  • [24] Tanış C., Saraçoğlu B., Kuş C., Pekgör A., Karakaya K., Transmuted lower record type Fréchet distribution with lifetime regression analysis based on type I-censored data, Journal of Statistical Theory and Applications, 20(1) (2021) 86-96.
  • [25] Shen Y., Xu A., On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods, Communications in Statistics-Theory and Methods, 47(22) (2018) 5558-5572.
  • [26] Lee K. R., Kapadia C. H., Brock D. B., On estimating the scale parameter of the Rayleigh distribution from doubly censored samples, Statistische Hefte, 21(1) (1980) 14-29.
  • [27] Tiku M. L., Akkaya A. D., Robust estimation and hypothesis testing, New Age International, (2004).
  • [28] Elgarhy M., Haq M. A. U., ul Ain Q., Exponentiated generalized Kumaraswamy distribution with applications, Annals of Data Science, 5 (2018) 273-292.

Year 2025, Volume: 46 Issue: 1, 179 - 184, 25.03.2025

Sümeyra Sert , Coşkun Kuş

https://doi.org/10.17776/csj.1460135

Abstract

References

  • [1] Adeoti O. A., Rao G. S., Attribute control chart for Rayleigh distribution using repetitive sampling under truncated life test, Journal of Probability and Statistics, (1) (2022) 8763091.
  • [2] Hossain M. P., Omar M. H., Riaz M., Arafat S. Y., On designing a new control chart for Rayleigh distributed processes with an application to monitor glass fiber strength, Communications in Statistics-Simulation and Computation, 51(6) (2022) 3168-3184.
  • [3] Anis M. Z., Okorie I. E., Ahsanullah M., A review of the Rayleigh distribution: properties, estimation & application to COVID-19 data, Bulletin of the Malaysian Mathematical Sciences Society, 47(1) (2024) 6.
  • [4] Aslam M., Jun C. H., A group acceptance sampling plan for truncated life test having Weibull distribution. Journal of Applied Statistics, 36(9) (2009) 1021-1027.
  • [5] Soliman A., Amin E. A., Abd-El Aziz A. A., Estimation and prediction from inverse Rayleigh distribution based on lower record values, Applied Mathematical Sciences, 4(62) (2010) 3057-3066.
  • [6] Prakash G., Shrinkage Estimation in the Inverse Rayleigh Distribution, Journal of Modern Applied Statistical Methods, 9 (2010) 209-220.
  • [7] Dey S., Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution, Malaysian Journal of Mathematical Sciences, 6(1) (2012) 113-124.
  • [8] Akdoğan Y., Özkan E., Karakaya K., Tanış C., Estimation Of Parameter For Inverse Rayleigh Distribution Under Type-I Hybrid Censored Samples, Sigma Journal of Engineering and Natural Sciences, 38(4) (2020) 1705-1711.
  • [9] Adeoti O. A., Gadde S. R., Moving average control charts for the Rayleigh and inverse Rayleigh distributions under time truncated life test, Quality and Reliability Engineering International, 37(8) (2021) 3552-3567.
  • [10] Athirakrishnan R. B., Abdul-Sathar E. I., E-Bayesian and hierarchical Bayesian estimation of inverse Rayleigh distribution, American Journal of Mathematical and Management Sciences, 41(1) (2022) 70-87.
  • [11] Kumar R., Gupta R., Bayesian analysis of inverse Rayleigh distribution under non-informative prior for different loss functions, Thailand Statistician, 21(1) (2023) 76-92.
  • [12] Karakaya K., Kınacı İ., Akdoğan Y., Saraçoğlu B., Kuş C., Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring, Pakistan Journal of Statistics and Operation Research, (2024) 37-47.
  • [13] Lalitha S., Mishra A., Modified maximum likelihood estimation for Rayleigh distribution, Communications in Statistics-Theory and Methods, 25(2) (1996) 389-401.
  • [14] Wingo D. R., Maximum likelihood estimation of Burr XII distribution parameters under type II censoring, Microelectronics Reliability, 33(9) (1993) 1251-1257.
  • [15] Balakrishnan N., Kundu D., Ng K. T., Kannan N., Point and interval estimation for a simple step-stress model with Type-II censoring, Journal of Quality Technology, 39(1) (2007) 35-47.
  • [16] Jaheen Z. F., Okasha H. M., E-Bayesian estimation for the Burr type XII model based on type-2 censoring, Applied Mathematical Modelling, 35(10) (2011) 4730-4737.
  • [17] Almetwally E. M., Sabry M. A., Alharbi R., Alnagar D., Mubarak S. A., Hafez E. H., Marshall–olkin alpha power Weibull distribution: different methods of estimation based on type-I and type-II censoring, Complexity, (2021) 1-18.
  • [18] Biçer H. D., Öztürker B., Estimation procedures on Type-II censored data from a scaled Muth distribution, Sigma Journal of Engineering and Natural Sciences, 39(2) (2021) 148-158.
  • [19] Schneider H., Weissfeld L. (1986). Inference based on Type II censored samples, Biometrics, 531-536.
  • [20] Balakrishnan N., Aggarwala R., Progressive censoring: theory, methods, and applications, Springer Science & Business Media, (2000).
  • [21] Karakaya K., Tanış C., Different methods of estimation for the one parameter Akash distribution, Cumhuriyet Science Journal, 41(4) (2020a) 944-950.
  • [22] Karakaya K., Tanış C., Estimating the parameters of Xgamma Weibull distribution, Adıyaman University Journal of Science, 10(2) (2020b) 557-571.
  • [23] Tanış C., Karakaya K., On Estimating Parameters of Lindley-Geometric Distribution, Eskişehir Technical University Journal of Science and Technology A-Applied Sciences and Engineering, 22(2) (2021) 160-167.
  • [24] Tanış C., Saraçoğlu B., Kuş C., Pekgör A., Karakaya K., Transmuted lower record type Fréchet distribution with lifetime regression analysis based on type I-censored data, Journal of Statistical Theory and Applications, 20(1) (2021) 86-96.
  • [25] Shen Y., Xu A., On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods, Communications in Statistics-Theory and Methods, 47(22) (2018) 5558-5572.
  • [26] Lee K. R., Kapadia C. H., Brock D. B., On estimating the scale parameter of the Rayleigh distribution from doubly censored samples, Statistische Hefte, 21(1) (1980) 14-29.
  • [27] Tiku M. L., Akkaya A. D., Robust estimation and hypothesis testing, New Age International, (2004).
  • [28] Elgarhy M., Haq M. A. U., ul Ain Q., Exponentiated generalized Kumaraswamy distribution with applications, Annals of Data Science, 5 (2018) 273-292.
There are 28 citations in total.

Details

Primary Language English
Subjects Statistical Analysis, Statistical Theory
Journal Section Natural Sciences
Authors

Sümeyra Sert 0000-0002-4647-1583

Coşkun Kuş 0000-0002-7176-0176

Publication Date March 25, 2025
Submission Date March 27, 2024
Acceptance Date February 4, 2025
Published in Issue Year 2025Volume: 46 Issue: 1

Cite

APA Sert, S., & Kuş, C. (2025). Point Estimation for the Inverse Rayleigh Distribution under Type-II Left and Right Censoring. Cumhuriyet Science Journal, 46(1), 179-184. https://doi.org/10.17776/csj.1460135
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