The presence of lower and upper outliers in the dataset may cause misleading inferential conclusions in applied statistical problems. This paper introduces the three-component mixture of exponential (3-CME) distributions as an alternative platform for analyzing positive datasets in the presence of multiple lower and upper outliers. We obtain the parameter estimates with focus on the Bayesian approach. In order to investigate the performance of the presented approach, five simulation studies are conducted. We show that the proposed outlier model can be selected as an appropriate alternative model in dealing with the data with and without lower and upper outliers. The performance of the Bayes estimators under dierent loss functions with various sample sizes and number of outliers is also investigated. Finally, two examples of real data are studied to illustrate the superiority of the 3-CME distributions in analyzing dataset and detecting lower and upper outliers.

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