Abstract
Inverted exponentiated exponential densities family is known for its flexibility and applicability in the reliability field. This study evaluates the performance of different estimation methods for the inverted exponentiated Pareto (IEP) distribution, which is a special case of this family of distributions. In this study, the parameter estimation of the IEP distribution is obtained using Maximum Likelihood (ML), Maximum Product of Spacings (MPS), Cramer von Mises (CvM), and Anderson Darling (AD) methods. A Monte Carlo simulation is conducted to compare the efficiency of these estimation methods, while real data applications from different fields are utilized to demonstrate practical performance. The fitting performance of the methods is assessed using metrics such as root mean squared error, coefficient of determination, Anderson Darling, and the Kolmogorov-Smirnov test. Simulation results indicate that the MPS method generally outperforms the ML and CvM methods, whereas real data applications reveal that the CvM method provides the best parameter estimates, followed by MPS.
Ethical Statement
The study is complied with research and publication ethics.
Project Number
-
References
- M. E. Ghitany, V. K. Tuan, and N. Balakrishnan, “Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data,” J Stat Comput Simul, vol. 84, no. 1, pp. 96–106, Jan. 2014, doi: 10.1080/00949655.2012.696117.
- H. Krishna and K. Kumar, “Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample,” J Stat Comput Simul, vol. 83, no. 6, pp. 1007–1019, Jun. 2013, doi: 10.1080/00949655.2011.647027.
- M. Dube, H. Krishna, and R. Garg, “Generalized inverted exponential distribution under progressive first-failure censoring,” J Stat Comput Simul, vol. 86, no. 6, pp. 1095–1114, Apr. 2016, doi: 10.1080/00949655.2015.1052440.
- R. K. Maurya, Y. M. Tripathi, T. Sen, and M. K. Rastogi, “Inference for an Inverted Exponentiated Pareto Distribution Under Progressive Censoring,” J Stat Theory Pract, vol. 13, no. 1, p. 2, 2018, doi: 10.1007/s42519-018-0002-y.
- F. Kızılaslan, “Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions,” Statistical Papers, vol. 59, no. 3, pp. 1161–1192, 2018, doi: 10.1007/s00362-016-0810-7.
- R. Kumari, Y. M. Tripathi, R. K. Sinha, and L. Wang, “Comparison of Estimation Methods for Reliability Function for Family of Inverse Exponentiated Distributions under New Loss Function,” Axioms, vol. 12, no. 12, 2023, doi: 10.3390/axioms12121096.
- R. K. Maurya, Y. M. Tripathi, T. Sen, and M. K. Rastogi, “On progressively censored inverted exponentiated Rayleigh distribution,” J Stat Comput Simul, vol. 89, no. 3, pp. 492–518, Feb. 2019, doi: 10.1080/00949655.2018.1558225.
- A. F. Hashem, S. A. Alyami, and M. M. Yousef, “Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data,” Axioms, vol. 12, no. 9, 2023, doi: 10.3390/axioms12090872.
- M. K. Rastogi and Y. M. Tripathi, “Estimation for an inverted exponentiated Rayleigh distribution under type II progressive censoring,” J Appl Stat, vol. 41, no. 11, pp. 2375–2405, Nov. 2014, doi: 10.1080/02664763.2014.910500.
- F. Jamal, C. Chesneau, and M. Elgarhy, “Type II general inverse exponential family of distributions,” Journal of Statistics and Management Systems, vol. 23, no. 3, pp. 617–641, Apr. 2020, doi: 10.1080/09720510.2019.1668159.
- H. Panahi and S. Asadi, “Estimation of the micro splat splashing data using the inverted exponentiated Rayleigh stress-strength reliability model,” Journal of Statistics and Management Systems, vol. 22, no. 8, pp. 1401–1416, Nov. 2019, doi: 10.1080/09720510.2019.1596594.
- L. Wang, Y. M. Tripathi, S.-J. Wu, and M. Zhang, “Inference for confidence sets of the generalized inverted exponential distribution under k-record values,” J Comput Appl Math, vol. 380, p. 112969, 2020, doi: https://doi.org/10.1016/j.cam.2020.112969.
- C. Lodhi, Y. M. Tripathi, and L. Wang, “Inference for a general family of inverted exponentiated distributions with partially observed competing risks under generalized progressive hybrid censoring,” J Stat Comput Simul, vol. 91, no. 12, pp. 2503–2526, Aug. 2021, doi: 10.1080/00949655.2021.1901290.
- R. Kumari, Y. M. Tripathi, R. K. Sinha, and L. Wang, “Reliability estimation for the inverted exponentiated Pareto distribution,” Qual Technol Quant Manag, vol. 20, no. 4, pp. 485–510, Jul. 2023, doi: 10.1080/16843703.2022.2125762.
- D. L. Donoho and R. C. Liu, “The" automatic" robustness of minimum distance functionals,” The Annals of Statistics, vol. 16, no. 2, pp. 552–586, 1988.
- D. Hinkley, “On quick choice of power transformation,” J R Stat Soc Ser C Appl Stat, vol. 26, no. 1, pp. 67–69, 1977.
- D. N. P. Murthy, Weibull models. Wiley, 2004.
Abstract
Bu çalışma, güvenilirlik alanında esnekliği ve uygulanabilirliği ile bilinen inverted exponentiated Pareto (IEP) dağılımı için farklı parametre tahmin yöntemlerinin performansını değerlendirmektedir. Bu çalışmada, IEP dağılımının parametre tahmini Maximum Likelihood (ML), Maximum Product of Spacings (MPS) Anderson Darling (AD) ve Cramer von Mises (CvM) yöntemleri kullanılarak gerçekleştirilmiştir. Bu yöntemlerin etkinliğini karşılaştırmak için Monte Carlo simülasyonu yapılmış ve farklı alanlardan gerçek veri uygulamaları kullanılarak metotların performansları gösterilmiştir. Yöntemlerin uyum performansı, kök ortalama kare hata, belirleme katsayısı ve Kolmogorov-Smirnov testi gibi metriklerle değerlendirilmiştir. Simülasyon sonuçları, MPS yönteminin genel olarak ML, AD ve CvM yöntemlerinden daha iyi performans gösterdiğini, gerçek veri uygulamalarının ise CvM yönteminin en iyi parametre tahminlerini sağladığını ve onu MPS'nin yakından takip ettiğini ortaya koymuştur.
Project Number
-
References
- M. E. Ghitany, V. K. Tuan, and N. Balakrishnan, “Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data,” J Stat Comput Simul, vol. 84, no. 1, pp. 96–106, Jan. 2014, doi: 10.1080/00949655.2012.696117.
- H. Krishna and K. Kumar, “Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample,” J Stat Comput Simul, vol. 83, no. 6, pp. 1007–1019, Jun. 2013, doi: 10.1080/00949655.2011.647027.
- M. Dube, H. Krishna, and R. Garg, “Generalized inverted exponential distribution under progressive first-failure censoring,” J Stat Comput Simul, vol. 86, no. 6, pp. 1095–1114, Apr. 2016, doi: 10.1080/00949655.2015.1052440.
- R. K. Maurya, Y. M. Tripathi, T. Sen, and M. K. Rastogi, “Inference for an Inverted Exponentiated Pareto Distribution Under Progressive Censoring,” J Stat Theory Pract, vol. 13, no. 1, p. 2, 2018, doi: 10.1007/s42519-018-0002-y.
- F. Kızılaslan, “Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions,” Statistical Papers, vol. 59, no. 3, pp. 1161–1192, 2018, doi: 10.1007/s00362-016-0810-7.
- R. Kumari, Y. M. Tripathi, R. K. Sinha, and L. Wang, “Comparison of Estimation Methods for Reliability Function for Family of Inverse Exponentiated Distributions under New Loss Function,” Axioms, vol. 12, no. 12, 2023, doi: 10.3390/axioms12121096.
- R. K. Maurya, Y. M. Tripathi, T. Sen, and M. K. Rastogi, “On progressively censored inverted exponentiated Rayleigh distribution,” J Stat Comput Simul, vol. 89, no. 3, pp. 492–518, Feb. 2019, doi: 10.1080/00949655.2018.1558225.
- A. F. Hashem, S. A. Alyami, and M. M. Yousef, “Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data,” Axioms, vol. 12, no. 9, 2023, doi: 10.3390/axioms12090872.
- M. K. Rastogi and Y. M. Tripathi, “Estimation for an inverted exponentiated Rayleigh distribution under type II progressive censoring,” J Appl Stat, vol. 41, no. 11, pp. 2375–2405, Nov. 2014, doi: 10.1080/02664763.2014.910500.
- F. Jamal, C. Chesneau, and M. Elgarhy, “Type II general inverse exponential family of distributions,” Journal of Statistics and Management Systems, vol. 23, no. 3, pp. 617–641, Apr. 2020, doi: 10.1080/09720510.2019.1668159.
- H. Panahi and S. Asadi, “Estimation of the micro splat splashing data using the inverted exponentiated Rayleigh stress-strength reliability model,” Journal of Statistics and Management Systems, vol. 22, no. 8, pp. 1401–1416, Nov. 2019, doi: 10.1080/09720510.2019.1596594.
- L. Wang, Y. M. Tripathi, S.-J. Wu, and M. Zhang, “Inference for confidence sets of the generalized inverted exponential distribution under k-record values,” J Comput Appl Math, vol. 380, p. 112969, 2020, doi: https://doi.org/10.1016/j.cam.2020.112969.
- C. Lodhi, Y. M. Tripathi, and L. Wang, “Inference for a general family of inverted exponentiated distributions with partially observed competing risks under generalized progressive hybrid censoring,” J Stat Comput Simul, vol. 91, no. 12, pp. 2503–2526, Aug. 2021, doi: 10.1080/00949655.2021.1901290.
- R. Kumari, Y. M. Tripathi, R. K. Sinha, and L. Wang, “Reliability estimation for the inverted exponentiated Pareto distribution,” Qual Technol Quant Manag, vol. 20, no. 4, pp. 485–510, Jul. 2023, doi: 10.1080/16843703.2022.2125762.
- D. L. Donoho and R. C. Liu, “The" automatic" robustness of minimum distance functionals,” The Annals of Statistics, vol. 16, no. 2, pp. 552–586, 1988.
- D. Hinkley, “On quick choice of power transformation,” J R Stat Soc Ser C Appl Stat, vol. 26, no. 1, pp. 67–69, 1977.
- D. N. P. Murthy, Weibull models. Wiley, 2004.
Details
| Primary Language | English |
|---|---|
| Subjects | Stochastic Analysis and Modelling, Applied Statistics |
| Journal Section | Research Article |
| Authors | |
| Project Number | - |
| Publication Date | March 26, 2025 |
| Submission Date | December 10, 2024 |
| Acceptance Date | March 20, 2025 |
| Published in Issue | Year 2025 Volume: 14 Issue: 1 |
