# Confidence Intervals for the Common Inverse Mean of Several Normal Populations with Unknown Coefficients of Variation

## Keywords:

GCI approach, Large sample approach, Adjusted MOVER approach## Abstract

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

## Downloads

## Published

## Issue

## Section

## License

Copyright Notice: a copyright on any article in the published journal is retained by the **Ramkhamhaeng International Journal of Science and Technology**. Readers or Users grant the right to use of the Article contained in the Content in accordance with the Creative Commons CC BY-NC-ND license and the Data contained in the Content in accordance with the Creative Commons CC BY-NC-ND.