ALTERNATIVE MEASURES OF CENTRAL TENDENCY

This paper presents two new estimators of the expectation of a random variable X, which are also unbiased and consistent as an arithmetic mean but more efficient. The first one is called center owing to the fact that its value is usually located between the mean and the median of the analyzed data. The second one is called C2 statistic. Both statistics are weighted averages. The center and C2 are computed with weights which are functions of the remoteness of each observation from other. Thus, these statistics use all available data in contrast to the median or a trimmed mean. They are less sensitive to the effect of outliers than the arithmetic mean because of the fact that the outlying observations receive smaller weights than these which are close to the median. The article presents mathematical and empirical proofs of the above statements.