A modified robust confidence interval for the population mean of distribution based on deciles

Moustafa Omar Ahmed Abu-Shawiesh; Juthaphorn Sinsomboonthong; Bhuiyan Mohammad Golam Kibria

doi:10.21307/stattrans-2022-007

A modified robust confidence interval for the population mean of distribution based on deciles

Moustafa Omar Ahmed Abu-Shawiesh Department of Mathematics, Faculty of Science, The Hashemite University, P. O. Box 330127, Zarqa 13133, Jordan ORCID:https://orcid.org/0000-0003-0618-7833 , Juthaphorn Sinsomboonthong Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand ORCID:https://orcid.org/0000-0002-3375-5982 , Bhuiyan Mohammad Golam Kibria Department of Mathematics and Statistics, Florida International University, University Park, Miami FL 33199, USA ORCID:https://orcid.org/0000-0002-6073-1978 Statistics in Transition new series, vol. 23, 2022, 1, pages: 109-128 Published online: 15 March 2022 DOI 10.21307/stattrans-2022-007 Citation: Abu-Shawiesh M. O. A., Sinsomboonthong J., Golam Kibria B. M., (2022).A modified robust confidence interval for the population mean of distribution based on deciles, Statistics in Transition new series, 23(1), pp. 109–128. https://doi.org/10.21307/stattrans-2022-007

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ABSTRACT

The confidence interval is an important statistical estimator of population location and dispersion parameters. The paper considers a robust modified confidence interval, which is an adjustment of the Student’s t confidence interval based on the decile mean and decile standard deviation for estimating the population mean of a skewed distribution. The efficiency of the proposed interval estimator is evaluated on the basis of an extensive Monte Carlo simulation study. The coverage ratio and average width of the proposed confidence interval are compared with certain existing and widely used confidence intervals. The simulation results show that, in general, the proposed interval estimator’s performance is highly effective. For illustrative purposes, three real-life data sets are analyzed, which, to a certain extent, support the findings obtained from the simulation study. Thus, we recommend that practitioners use the robust modified confidence interval for estimating the population mean when the data are generated by a normal or skewed distribution.

KEYWORDS

robust confidence interval, decile mean, decile mean standard deviation, decile mean standard error, Monte Carlo simulation

REFERENCES

Abu-Shawiesh, M. O. A., Al-Athari, F. M., Kittani, H. F., (2009). Confidence interval for the mean of a contaminated normal distribution, Journal of Applied Sciences, Vol. 9(15), pp. 2835–2840.

Abu-Shawiesh, M. O. A., Banik, S., Kibria, B. G., (2011). A simulation study on some confidence intervals for the population standard deviation, SORT-Statistics and Operations Research Transactions, Vol. 35(2), pp. 83–102.

Abu-Shawiesh, M. O. A., Banik, B., Kibria, B. M. G., (2018). Confidence Intervals based on absolute deviation for population mean of a positively skewed distribution, International Journal of Computational and Theoretical Statistics, Vol. 5(1), pp. 1–13.

Abu-Shawiesh, M. O. A., Saghir, A., (2019). Robust confidence intervals for the population mean alternatives to the Student-t confidence interval, Journal of Modern Applied Statistical Methods, Vol. 18(1), pp. 1–21.

Akyuz, H. E., Abu-Shawiesh, M. O. A., (2020). A robust confidence interval based on modified trimmed standard deviation for the mean of positively skewed populations, Electronic Journal of Applied Statistical Analysis, Vol. 13(1), pp. 164–182.

Baklizi, A., Kibria, B. M. G., (2009). One and two sample confidence intervals for estimating the mean of skewed populations: An empirical comparative study, Journal of Applied Statistics, Vol. 36(6), pp. 601–609.

Banik, S., Kibria, B. M. G., (2010). Comparison of some parametric and nonparametric type one sample confidence intervals for estimating the mean of a positively skewed distribution, Communications in Statistics-Simulation and Computation, Vol. 39(2), pp. 361–389.

Berndt, C. C., (1989). Instrumented tensile adhesion tests on plasma sprayed thermal barrier coatings, Journal of Materials Engineering, Vol. 11(4), pp. 275–282.

Boos, D., And Hughes-Oliver, J., (2000). How large does n have to be for Z and t intervals, The American Statistician, Vol. 54(2), pp. 121–128.

Cain, M. K., Zhang, Z., Yuan, K. H., (2016). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation, Behavior Research Methods, Vol. 49(5), pp. 1716–1735.

Chen, L., (1995). Testing the mean of skewed distributions, Journal of the American Statistical Association, Vol. 90(430), pp. 767–772.

Diciccio, T. J., Efron, B., (1996). Bootstrap confidence intervals, Statistical Science, Vol. 11(3), pp. 189–228.

Doulah, M. S. U., (2018). Alternative measures of standard deviation coefficient of variation and standard error, International Journal of Statistics and Applications, Vol. 8(6), pp. 309–315.

Efron, B., Tibshirani, R. J., (1993). An Introduction to the Bootstrap, London: Chapman & Hall.

Gastwirth, J. L., (1982). Statistical Properties of a Measure of Tax Assessment Uniformity, Journal of the Statistical Inference and Planning, Vol. 6(1), pp. 1–12.

Ghosh, S., Polansky, A. M., (2016). New bootstrap confidence interval for means of a positively skewed distributions, Communications in Statistics-Theory and Methods, Vol. 45(23), pp. 6915–6927.

International Olympic Committee, (2019). London 2012 long jump men – Olympic athletics. Retrieved from https://www.olympic.org/london2012/athletics/longjump- men.

Johnson, N. J., (1978). Modified t-tests and confidence intervals for asymmetrical population, Journal of the American Statistical Association, Vol. 73(363), pp. 536– 544.

Johnson, R. E., Mcfarland, B. H., (1993). Antipsychotic drug exposure in a health maintenance organization, Medical Care, Vol. 31(5), pp. 432–444.

Kibria, B. M. G., (2006). Modified confidence intervals for the mean of the asymmetric distribution, Pakistan Journal of Statistics, Vol. 22(2), pp. 109–120.

Luh, W., Guo, J., (2001). Transformation works for non-normality? On one-sample transformation trimmed t methods, British Journal of Mathematical and Statistical Psychology, Vol. 54(2), pp. 227–236.

Marinho, P. R. D., Cordeiro, G. M., Pena, R., Alizadeh, M., Bourguignon, M., (2018). The exponentiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap, Brazilian Journal of Probability and Statistics, Vol. 32(2), pp. 281–308.

Mcdonald, J. H., (2014). Handbook of Biological Statistics, 3rd ed., Maryland: Sparky House Publishing.

Meeden, G., (1999). Interval estimators for the population mean for skewed distributions with a small sample size, Journal of Applied Statistics, Vol. 26(1), pp. 81–96.

Miller, J. M., Penfield, R. D., (2005). Using the score method to construct asymmetric confidence intervals: An SAS program for content validation in scale development, Behavior Research Methods, Vol. 37(3), pp. 450–452.

Mudelsee, M., Alkio, M., (2007). Quantifying effects in two-sample environmental experiments using bootstrap confidence intervals, Environmental Modelling and Software, Vol. 22(1), pp. 84–96.

Neyman, J., (1937). Outline of a theory of statistical estimation based on the classical theory of probability, Philosophical Transactions of the Royal Society Series A, Vol. 236(767), pp. 333–380.

Pek, J., Wong, A.C.M., Wong, O., (2017). Confidence intervals for the mean of nonnormal distribution: Transform or not to transform, Open Journal of Statistics, Vol. 7(3), pp. 405–421.

Rana, S., Doulah, M. S. U., Midi, H., Imon, A. H. M. R., (2012). Decile mean: a new robust measure of central tendency, Chiang Mai Journal of Sciences, Vol. 39(3), pp. 478–485.

Sharma, K. K., Kumar, A., Chaudhary, A., (2009). Statistics in Management Studies. India: Krishna Media (P) Ltd.

Shi, W., Kibria, B. M. G., (2007). On some confidence intervals for estimating the mean of a skewed population, International Journal of Mathematical Education in Science and Technology, Vol. 38(3), pp. 412–421.

Sindhumol, M. R., Srinivasan, M. M., Gallo, M., (2016). Robust control charts based on modified trimmed standard deviation and Gini's mean difference, Journal of Applied Quantitative Methods, Vol. 11(3), pp. 18–30.

Sinsomboonthong, J., Abu-Shawiesh, M. O. A., Kibria, B. M. G., (2020). Performance of robust confidence intervals for estimating population mean under both nonnormality and in presence of outliers, Advances in Science, Technology and Engineering Systems Journal, Vol. 5(3), pp. 442–449.

Student, (1908). The probable error of a mean, Biometrika, Vol. 6(1), pp. 1–25.

Yanagihara, H., Yuan, K. H. (2005). Four improved statistics for contrasting means by correcting skewness and kurtosis, British Journal of Mathematical and Statistical Psychology, Vol. 58(2), pp. 209-237.