### Journals Information

Mathematics and Statistics Vol. 12(1), pp. 31 - 40
DOI: 10.13189/ms.2024.120105
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## A New Robust Interval Estimation for the Median of An Exponential Population When Some of the Observations are Extreme Values

Faris Muslim Al-Athari *
Department of Financial and Banking Sciences, AL-Turath University College, Iraq

ABSTRACT

The issue of obtaining accurate interval estimates for the median of an exponential population when some of the observations are extreme values is an important issue for researchers in the fields of reliability applications and survival analysis. In this research paper, a new method is proposed for obtaining a robust confidence interval which is a substitute for the known ordinary (classical) confidence interval when there are extreme values in the sample. The proposed method is simply a result of changing the sample mean by a constant multiple of a sample median and adjusting the upper percentile point of the chi-square of the ordinary confidence interval formula. Further, the performance of the proposed method is evaluated and compared with the ordinary one by using Monte Carlo simulation based on 100,000 trials for each sample size with 5% and 10% extreme values showing that the proposed method, under the contaminated exponential distribution, is always performing better than the ordinary method in the sense of having simulated confidence probability quite close to the aimed confidence level with shorter width and smaller standard error. The use and the application of the proposed method to real-life data are presented and compared with the simulation results.

KEYWORDS
Exponential Distribution, Robustness, Median Estimates, Confidence Probability, Standard Error, Extreme Values, Coverage Probability

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Faris Muslim Al-Athari , "A New Robust Interval Estimation for the Median of An Exponential Population When Some of the Observations are Extreme Values," Mathematics and Statistics, Vol. 12, No. 1, pp. 31 - 40, 2024. DOI: 10.13189/ms.2024.120105.

(b). APA Format:
Faris Muslim Al-Athari (2024). A New Robust Interval Estimation for the Median of An Exponential Population When Some of the Observations are Extreme Values. Mathematics and Statistics, 12(1), 31 - 40. DOI: 10.13189/ms.2024.120105.