Asymptotic sampling distribution of inverse coe?cient of variation and its applications: revisited


  • Ahmed N. Albatineh Florida International University
  • B.M Golam Kibria Florida International University Department of Mathematics and Statistics
  • Bashar Zogheib American University of Kuwait Department of Mathematics and Natural Sciences





Sharma and Krishna (1994) derived mathematically an appealing asymptotic confidence interval for the population signal-to-noise ratio (SNR). In this paper, an evaluation of the performance of this interval using monte carlo simulations using randomly generated data from normal, log-normal, $\chi^2$, Gamma, and Weibull distributions three of which are discussed in Sharma and Krishna (1994). Simulations revealed that its performance, as measured by coverage probability, is totally dependent on the amount of noise introduced. A proposal for using ranked set sampling (RSS) instead of simple random sampling (SRS) improved its performance. It is recommended against using this confidence interval for data from a log-normal distribution. Moreover, this interval performs poorly in all other distributions unless the SNR is around one.

Keywords: Signal-to-noise ratio, coefficient of variation, sampling distribution, confidence interval, ranked set sample, simple random sample.



Bernatm, D.H., Lazovich, D., Forster, J.L., Oakes, J.M., Chen, V., Area-level variation in adolescent smoking, Preventing Chronic Disease, 6, 2, (2009) 1-8.

Faber, D. S. and Korn, H., Applicability of the coefficient of variation for analyzing synaptic plasticity, Biophysical Society, 60, (1991) 1288-1294.

George. F. and Kibria, B. M. Golam, Confidence intervals for estimating the population signal-to-noise ratio: a simulation study, Journal of Applied Statistics, 39, (2012) 1225-1240.

Gulhar, M., Kibria, B. M. G., Albatineh, A. N., and Ahmed, N. U. , A Comparison of some confidence intervals for estimating the population coefficient of variation: a simulation study, SORT, 36, (2012) 45 - 68.

Kang, K. and Schmeiser, B. W., Methods for evaluating and comparing confidence interval procedures, Technical Report, Dept. Industrial Engineering, University of Miami, Florida, U.S.A, (1986).

Kelly, K. , Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach, Behavior Research Methods, 39, 4, (2007) 755-766.

MacEachern, S., Ozturk, O., and Wolfe, D.A., A New ranked set sample estimator of variance, Journal of the Royal Statistical Society B., 64, Part 2, (2002) 177 - 188.

Mahmoudvand, R. and Hassani, H., Two new confidence intervals for the coefficient of variation, Journal of Applied Statistics, 36, (2009) 429 - 442.

McIntyre, G. A., A Method for unbiased selective sampling using ranked sets, Australian Journal of Agricultural Research, 3, (1952) 385 - 390.

McGibney, G. and Smith, M. R., An unbiased signal-to-noise ratio measure for magnetic resonance images, Medical Physics, 20, (1993) 1077-1078.

Panichkitkosolkul, W., Asymptotic confidence interval for the coefficient of variation of Poisson distribution: a simulation study, Maejo International Journal of Science and Technology, 4, (2010) 1 - 7.

Panichkitkosolkul, W., Improved confidence intervals for a coefficient of variation of a normal distribution, Thailand Statistician, 7, (2009) 193 - 199.

R Development Core Team, R: A language and environment for statistical computing, R foundation for statistical computing, Vienna, Austria. ISBN 3-900051-07-0, URL, (2007).

Samawi, H. M. and Muttlak, H. A., Estimation of ratio using ranked set sampling, Biometrical Journal, 6, (1996) 753 – 76.

Samawi, H. M., More efficient Monte Carlo Methods obtained by using ranked set simulated samples, Communications in Statistics - Simulation and Computation, 28, (1999) 699 - 713.

Sharma, K. K. and Krishna, H., Asymptotic sampling distribution of inverse coefficient- of -variation and its applications. IEEE Transactions on Reliability, 43, (1994) 630 - 633.

Stokes, S.L., Estimation of variance using judgment ordered ranked set samples, Biometrics, 36, (1980) 35-42.

Takahashi, K. and Wakimoto, K., On unbiased estimates of the population mean based on the sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics, 20, (1968) 1 - 31.

Terpstra, J. and Nelson, E., Optimal rank set sampling estimates for a population proportion, Journal of Statistical Planning and Inference, 127, (2005) 309 - 321.

Terpstra, J. and Wang, P., Confidence intervals for a population proportion based on a ranked set sample, Journal of Statistical Computation and Simulation, 78, (2008) 351-366.

View Full Article: