SOME STATISTICAL PROPERTIES OF POWER AVERAGES FOR LOGNORMAL SAMPLES

Power averages are often used to estimate the effective permeability o f a region based on sample measurements. Since the average is computed from a limited number of samples, it may suffer bias and sampling var iation. Expressions for bias and sampling variation are derived here f or averages having any exponent value between +1 (arithmetic average) and -1 (harmonic average). The derivations assume independent, lognorm ally distributed samples. The expressions agree with known results for the arithmetic, geometric, and harmonic averages. Estimator bias is g enerally smaller than 15% for common levels of permeability variabilit y and sample numbers. Sampling variability, however, may be a consider able fraction of the true mean. If sampling schemes aim to collect suf ficient data to keep the harmonic average within acceptable tolerances , other averages will meet or better that tolerance.