Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the γ-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights. Monte Carlo simulations showed that the γ-weighted geometric mean possesses low variance: smaller than the variance of the 0.20-trimmed mean for the Lomax distribution. The bias of the new statistic was also studied. We studied the bias in terms of nonparametric confidence intervals for the quantiles which correspond of our statistic for the case of the Lomax distribution. Deviation from the median for the γ-weighted geometric mean was measured in terms of the MSE for the log-logistic distribution and the Nakagami distri- bution (the MSE for the γ-weighted geometric mean was comparable or smaller than the MSE for the sample median).
Weighted Geometric Mean and its Properties,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
1, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss1/3