International Journal of Nonlinear Analysis and Applications
Construction confidence interval for a linear combination of parameters of the two-parameter exponential distribution under type II progressive censoring
Document Type : Research Paper
Author
aDepartment of Computer Science and Statistics, Faculty of Mathematics, K. N. Toosi university of Technology, P.O. Box 16765-3381, Tehran, Iran
Abstract
In this paper, to establish general and shortest confidence interval, for a linear combination of parameters of the two-parameter exponential distribution, we introduce a pivotal quantity. In the case of two populations, we use the method of variance estimate recovery and generalized pivotal quantities to construct a confidence interval for the difference of them. Based on the shortest confidence interval, we present a simple method to obtain its percentiles, and which a shorter confidence interval can be constructed. Also, the performances of the presented methods are studied by real data examples and simulations.
Keywords
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[13] K. Krishnamoorthy, Modified normal-based approximation to the percentiles of linear combination of independent random variables with applications, Comm. Stat. Simulat. Comput. 45 (2016), 2428–2444.
[14] K. Krishnamoorthy and T. Mathew, Statistical Tolerance Regions: Theory, Applications and Computation, Hoboken, NJ: Wiley, 2009.
[15] K. Krishnamoorthy and E. Oral, Standardized Likelihood Ratio Test for Comparing Several Log-normal Means and Confidence Interval for Conmen Mean, Stat. Meth. Med. Res. 1 (2015), no. 1, 1–23.
[16] K. Krishnamoorthy and Y. Xia, Confidence Intervals for a Two-parameter Exponential Distribution: One and Two-Sample Problems, Comm. Stat. Theor. Meth. 47 (2018), no. 4, 935–952.
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[25] R. Viveros and N. Balakrishnan, Interval estimation of parameters of life from progressively censored data, Technometrics 36 (1994), 84–91.
[26] S. Weerahandi, Generalized confidence intervals, J. Am. Stat. Assoc. 88 (1993) 899–905.
[27] G.Y. Zou and A. Donner, Construction of confidence limits about effect measures: A general approach, Stat. Med. 27 (2008), 1693–1702.
[28] G.Y. Zou, W. Huang and X. Zhang, A note on confidence interval estimation for a linear function of binomial proportions, Comput. Stat. Data Anal. 53 (2009), no. 4, 1080–1085.
[20] V. Maurya, A. Goyal and A.N. Gill, Multiple comparisons with more than one control for exponential location parameters under heteroscedasticity, Comm. Stat. Simulat. Comput. 40 (2011), 621–644.
[21] D.S. Paolino, Exact inference for the pth-quantile and the reliability of the two-parameter exponential distribution with singly type II censoring: a standard approach, Comm. Stat. Theor. Meth. 39 (2010), 2561–2572.
[22] J. Poirier, G.Y. Zou and J. Koval, Confidence Intervals for a Difference Between Log-Normal Means in Cluster Randomization Trials, Stat. Meth. Med. Res. 1 (2014), no. 1, 1–17.
[23] M. Roozbeh and M. Najarian, Which parts of generalized exponential distribution contain more information about parameters, Adv. Math.: Sci. J. 9 (2020), no. 9, 7407–7416.
[24] A. Roy and T. Mathew, A Generalized confidence limit for the reliability function of a two-parameter exponential distribution, J. Stat. Plann. Infer. 128 (2005), 509–517.
[25] R. Viveros and N. Balakrishnan, Interval estimation of parameters of life from progressively censored data, Technometrics 36 (1994), 84–91.
[26] S. Weerahandi, Generalized confidence intervals, J. Am. Stat. Assoc. 88 (1993) 899–905.
[27] G.Y. Zou and A. Donner, Construction of confidence limits about effect measures: A general approach, Stat. Med. 27 (2008), 1693–1702.
[28] G.Y. Zou, W. Huang and X. Zhang, A note on confidence interval estimation for a linear function of binomial proportions, Comput. Stat. Data Anal. 53 (2009), no. 4, 1080–1085.
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Volume 14, Issue 1
January 2023Pages 3071-3082
- Receive Date: 24 April 2021
- Revise Date: 11 December 2021
- Accept Date: 26 December 2021