The application of a doubly Type-Ⅱ censoring scheme, where observations are censored at both the left and right ends, is often used in various fields including social science, psychology, and economics. However, the observed sample size under this censoring scheme may not be large enough to apply a likelihood-based approach due to the occurrence of censoring at both ends. To effectively respond to this difficulty, we propose a pivotal-based approach within a doubly Type-Ⅱ censoring framework, focusing on two key aspects: Estimation for parameters of interest and prediction for missing or censored samples. The proposed approach offers two prominent advantages, compared to the likelihood-based approach. First, this approach leads to exact confidence intervals for unknown parameters. Second, it addresses prediction problems in a closed-form manner, ensuring computational efficiency. Moreover, novel algorithms using a pseudorandom sequence, which are introduced to implement the proposed approach, have remarkable scalability. The superiority and applicability of the proposed approach are substantiated in Monte Carlo simulations and real-world case analysis through a comparison with the likelihood-based approach.
Citation: Young Eun Jeon, Yongku Kim, Jung-In Seo. Predictive analysis of doubly Type-Ⅱ censored models[J]. AIMS Mathematics, 2024, 9(10): 28508-28525. doi: 10.3934/math.20241383
The application of a doubly Type-Ⅱ censoring scheme, where observations are censored at both the left and right ends, is often used in various fields including social science, psychology, and economics. However, the observed sample size under this censoring scheme may not be large enough to apply a likelihood-based approach due to the occurrence of censoring at both ends. To effectively respond to this difficulty, we propose a pivotal-based approach within a doubly Type-Ⅱ censoring framework, focusing on two key aspects: Estimation for parameters of interest and prediction for missing or censored samples. The proposed approach offers two prominent advantages, compared to the likelihood-based approach. First, this approach leads to exact confidence intervals for unknown parameters. Second, it addresses prediction problems in a closed-form manner, ensuring computational efficiency. Moreover, novel algorithms using a pseudorandom sequence, which are introduced to implement the proposed approach, have remarkable scalability. The superiority and applicability of the proposed approach are substantiated in Monte Carlo simulations and real-world case analysis through a comparison with the likelihood-based approach.
| [1] |
A. J. Fernández, Bayesian inference from type Ⅱ doubly censored Rayleigh data, Stat. Probabil. Lett., 48 (2000), 393–399. https://doi.org/10.1016/S0167-7152(00)00021-3 doi: 10.1016/S0167-7152(00)00021-3
|
| [2] |
M. Z. Raqab, M. T. Madi, Bayesian prediction of the total time on test using doubly censored Rayleigh data, J. Stat. Comput. Sim., 72 (2002), 781–789. https://doi.org/10.1080/00949650214670 doi: 10.1080/00949650214670
|
| [3] |
H. M. R. Khan, S. B. Provost, A. Singh, Predictive inference from a two-parameter Rayleigh life model given a doubly censored sample, Commun. Stat.-Theor. M., 39 (2010), 1237–1246. https://doi.org/10.1080/03610920902871453 doi: 10.1080/03610920902871453
|
| [4] |
C. Kim, S. Song, Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples, Stat. Pap., 51 (2010), 583–597. https://doi.org/10.1007/s00362-008-0142-3 doi: 10.1007/s00362-008-0142-3
|
| [5] |
M. S. Kotb, M. Z. Raqab, Inference and prediction for modified Weibull distribution based on doubly censored samples, Math. Comput. Simulat., 132 (2017), 195–207. https://doi.org/10.1016/j.matcom.2016.07.014 doi: 10.1016/j.matcom.2016.07.014
|
| [6] |
H. Panahi, Estimation for the parameters of the Burr Type Ⅻ distribution under doubly censored sample with application to microfluidics data, Int. J. Syst. Assur. Eng., 10 (2019), 510–518. https://doi.org/10.1007/s13198-018-0735-8 doi: 10.1007/s13198-018-0735-8
|
| [7] | T. N. Sindhu, Z. Hussain, Objective Bayesian analysis for the power function Ⅱ distribution under doubly type Ⅱ censored data, Thail. Statist., 20 (2022), 710–731. |
| [8] |
S. F. Wu, Interval estimation for the two-parameter exponential distribution based on the doubly type Ⅱ censored sample, Qual. Quant., 41 (2007), 489–496. https://doi.org/10.1007/s11135-006-9008-8 doi: 10.1007/s11135-006-9008-8
|
| [9] |
S. F. Wu, Interval estimation for a Pareto distribution based on a doubly type Ⅱ censored sample, Comput. Stat. Data An., 52 (2008), 3779–3788. https://doi.org/10.1016/j.csda.2007.12.015 doi: 10.1016/j.csda.2007.12.015
|
| [10] |
S. Weerahandi, Generalized confidence intervals, J. Am. Stat. Assoc., 88 (1993), 899–905. https://doi.org/10.2307/2290779 doi: 10.2307/2290779
|
| [11] | S. Weerahandi, Generalized inference in repeated measures: Exact methods in MANOVA and mixed models, New York: John Wiley & Sons, 2004. |
| [12] |
H. Alsuhabi, I. Alkhairy, E. M. Almetwally, H. M. Almongy, A. M. Gemeay, E. H. Hafez, et al., A superior extension for the Lomax distribution with application to Covid-19 infections real data, Alex. Eng. J., 61 (2022), 11077–11090. https://doi.org/10.1016/j.aej.2022.03.067 doi: 10.1016/j.aej.2022.03.067
|
| [13] |
Z. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Stat. Probabil. Lett., 49 (2000), 155–161. https://doi.org/10.1016/S0167-7152(00)00044-4 doi: 10.1016/S0167-7152(00)00044-4
|
| [14] |
B. X. Wang, K. Yu, M. C. Jones, Inference under progressively type Ⅱ right-censored sampling for certain lifetime distributions, Technometrics, 52 (2010), 453–460. https://doi.org/10.1198/TECH.2010.08210 doi: 10.1198/TECH.2010.08210
|
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Young Eun Jeon, Yongku Kim, Jung-In Seo. Predictive analysis of doubly Type-Ⅱ censored models[J]. AIMS Mathematics, 2024, 9(10): 28508-28525. doi: 10.3934/math.20241383
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