For data mining, outlier identification depends on distance measurements, grouping, and statistical approaches. The outliers change the behavior of the data and cause a serious error in the estimated results, that is why the parameters will be estimated after eliminating the effect. Outlying values have been an issue of concern to researchers and data analysts. The outliers will be detected and find out the effect of outliers and define how outliers affect the data set. Some methods will be used like MME and MLE to estimate the parameters of different distributions having outlier effects. The behavior of the parameters will be discussed in this research as then eliminate the outlier’s effect on the data set. The study of multiple outliers is imperative although outlying values can contribute to misrepresentation of the formula, wrong parameterization, and inaccurate summary statistics. A simulated study was carried out to investigate the strength of the test statistics. Exponential distribution discussed and calculated their parameters in size-biased as well as area-biased functions. The outliers have been discussed in this research by using discordancy tests. The graphical representation is used to differentiate the behavior of scale and shape parameters. The outliers have been detected with the help of the discordancy test for the single outlier as well as for two outliers and the results.