Confidence Intervals for the Common Inverse Mean of Several Normal Populations with Unknown Coefficients of Variation
Keywords:
GCI approach, Large sample approach, Adjusted MOVER approachAbstract
This paper proposes confidence intervals for the common inverse mean of the normal distributions with unknown coefficients of variation (CVs). The generalized confidence interval (GCI), large sample, adjusted method of variance estimates recovery (adjusted MOVER) approaches were proposed to construct the confidence intervals. The confidence intervals were compared with existing confidence interval for the common inverse mean of the normal distributions based on the GCI proposed by Thangjai et al. (2017a). The coverage probability and average length of the proposed confidence intervals were considered for performance criterion. The results indicate that the GCI and the adjusted MOVER confidence interval perform satisfactorily in terms of the coverage probability and average length for large sample sizes. The GCI and the adjusted MOVER approaches are better than the other approaches for constructing the confidence intervals for the common inverse mean of the normal distributions with unknown CVs. Finally, two real data in finance and medical science are given to illustrate the proposed confidence intervals.
References
Braulke M (1982) A note on the Nerlove model of agricultural supply response. International Economic Review 23: 241--246
Brown CS, Goodwin PC, Sorger PK (2001) Image metrics in the statistical analysis of DNA microarray data. Proceedings of the National Academy of Sciences of the United States of America 98: 8944--8949
Chaturvedi A, Rani U (1996) Fixed-width confidence interval estimation of the inverse coefficient of variation in a normal population. Microelectronics and Reliability 36: 1305--1308
Duerr D (2008) Design factors for fabricated steel below-the-hook lifting devices. Practice Periodical on Structural Design and Construction 13: 48--52
Fung WK, Tsang TS (1998) A simulation study comparing tests for the equality of coefficients of variation. Statistics in Medicine 17: 2003--2014
Graybill FA, Deal RB (1959) Combining unbiased estimators. Biometrics 15: 543--550
Johnson NL, Kotz S (1970) Distributions in Statistics: Continuous Univariate Distributions. Houghton Mifflin Company, Boston
Lamanna E, Romano G, Sgarbi C (1981) Curvature measurements in nuclear emulsions. Nuclear Instruments and Methods in Physics Research 187: 387--391
Niwitpong S, Wongkhao A (2015) Confidence interval for the inverse of normal mean. Far East Journal of Mathematical Sciences 98: 689--698
Niwitpong S, Wongkhao A (2016) Confidence intervals for the difference between inverse of normal means. Advances and Applications in Statistics 48: 337--347
Sahai A (2004) On an estimator of normal population mean and UMVU estimation of its relative efficiency. Applied Mathematics and Computation 152: 701--708
Sahai A, Acharya RM (2016) Iterative estimation of normal population mean using computational-statistical intelligence. Computational Science and Techniques 4: 500--508
Srivastava VK (1980) A note on the estimation of mean in normal population. Metrika 27: 99--102
Sodanin S, Niwitpong S, Niwitpong S (2016) Generalized confidence intervals for the normal mean with unknown coefficient of variation. AIP Conference Proceedings 1775: 030043--1-030043-8
Tian L (2005) Inferences on the common coefficient of variation. Statistics in Medicine 24: 2213--2220
Tian L, Wu J (2007) Inferences on the common mean of several log-normal populations: The generalized variable approach. Biometrical Journal 49: 944--951
Thangjai W, Niwitpong S (2017) Confidence intervals for the weighted coefficients of variation of two-parameter exponential distributions. Cogent Mathematics: 4: 1--16
Thangjai W, Niwitpong S, Niwitpong S (2016) Inferences on the common inverse mean of normal distribution. AIP Conference Proceedings 1775: 030027-1--030027-8
Thangjai W, Niwitpong S, Niwitpong S. (2017a) On large sample confidence intervals for the common inverse mean of several normal populations. Advances and Applications in Statistics 51: 59--84
Thangjai W, Niwitpong S, Niwitpong S (2017b) Confidence intervals for mean and difference of means of normal distributions with unknown coefficients of variation. Mathematics 5: 1--23
Thangjai W, Niwitpong S, Niwitpong S (2019) Confidence intervals for the inverse mean and difference of inverse means of normal distributions with unknown coefficients of variation. Studies in Computational Intelligence 808: 245--263
Treadwell E (1982) A momentum calculation for charges tracks with minute curvature. Nuclear Instruments and Methods 198: 337--342
Walpole RE, Myers RH, Myers SL, Ye K (2012) Probability and Statistics for Engineers and Scientists. Prentice Hall, New Jersey
Weerahandi S (1993) Generalized confidence intervals. Journal of American Statistical Association 88: 899--905
Withers CS, Nadarajah S (2013) Estimators for the inverse powers of a normal mean. Journal of Statistical Planning and Inference 143: 441--455
Wongkhao A, Niwitpong S, Niwitpong S (2013) Confidence interval for the inverse of a normal mean with a known coefficient of variation. International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering 7: 877--880
Ye RD, Ma TF, Wang SG (2010) Inferences on the common mean of several inverse Gaussian populations. Computational Statistics and Data Analysis 54: 906--915
Zou GY, Donner A (2008) Construction of confidence limits about effect measures: A general approach. Statistics in Medicine 27: 1693--1702
Zou GY, Taleban J, Hao CY (2009) Confidence interval estimation for lognormal data with application to health economics. Computation Statistics and Data Analysis 53: 3755--3764
Zubeck H, Kvinson TS (1996) Prediction of low-temperature cracking of asphalt concrete mixtures with thermal stress restrained specimen test results. Journal of the Transportation Research Board 1545: 50--58
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