Interval Estimation of the Overlapping Coefficient of Two Normal Distributions: One Way ANOVA with Random Effects
Keywords:
Overlapping coefficient, generalized pivotal quantity, one way random model, coverage probabilityAbstract
We consider the problem of deriving confidence interval for the Overlapping Coefficient (OVL) between one way random model with balanced and unbalanced data. The confidence intervals are derived using the concept of a Generalized Pivotal Quantity (GPQ). The accuracy of the proposed solutions are assessed using estimated coverage probabilities, and are also compared with other approximate solutions. The numerical results show that the GPQ method performs well in the estimation of OVL of two normal distributions under one way random model set-up. The results are illustrated with simulated examples.
References
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Roy A, Mathew T. A generalized confidence limit for the reliability function of a two parameter exponential distribution. J Stat Plann Infer. 2005; 128: 1-7.
Weerahandi S. Generalized confidence intervals. J Am Stat Assoc. 1993; 88: 899-905.
Weerahandi S. Exact statistical methods for data analysis. New York: Springer; 1994.
Weerahandi S. Generalized inference in repeated measures: Exact methods in MANOVA and mixed models. New Jersey: Wiley; 2004.
Krishnamoorthy K., Mathew T. Assessing Occupational exposure via the one way random effects model with balanced data. J Agric Biol Environ Statist. 2002; 4: 440-457.
Krishnamoorthy K, Mathew T. Inferences on the means of log normal distributions using generalized p-values and generalized confidence Intervals. J Stat Plann Infer. 2003; 115: 103-121.
Krishnamoorthy K, Mathew T. One sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals. Technometrics. 2004; 46: 44-52.
Kromhout H, Symanski E, Rappaport SM. A comprehensive evaluation of within and between worker components of occupational exposure to chemical agents. Ann Occup Hyg. 1993; 37: 253-270.
Lyles RH, Kupper LL, Rappaport SM. Assessing regulatory compliance of occupational exposures via the balanced one way random effects ANOVA model. J Agric Biol Environ Statist. 1997; 2: 64-86.
Minami M, Shimizu K. Estimation of similarity measure for multivariate normal distributions. Environ Ecol Stat. 1999; 6: 229-248.
Roy A, Mathew T. A generalized confidence limit for the reliability function of a two parameter exponential distribution. J Stat Plann Infer. 2005; 128: 1-7.
Weerahandi S. Generalized confidence intervals. J Am Stat Assoc. 1993; 88: 899-905.
Weerahandi S. Exact statistical methods for data analysis. New York: Springer; 1994.
Weerahandi S. Generalized inference in repeated measures: Exact methods in MANOVA and mixed models. New Jersey: Wiley; 2004.
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Published
2018-12-27
How to Cite
Jose, S., & Thomas, S. (2018). Interval Estimation of the Overlapping Coefficient of Two Normal Distributions: One Way ANOVA with Random Effects. Thailand Statistician, 17(1), 84–92. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/163204
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