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

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