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Modification of the adaptive kernel density estimation of income distribution and poverty index using the arithmetic mean

The new estimator is constructed with adaptive kernel and the bandwidth of the new improvement is obtained depending on the arithmetic mean of the observations. A simulated example is presented, including comparisons with three others estimators. The performance of the proposed new estimator is evaluated via the variance and the mean square error criterion. The results of the simulation study were very promising; they show that our modified estimator performs well in all cases.