Estimating the distribution of a variable measured with error: stand densities in a forest inventory

Abstract

If a variable is measured (or estimated) with error, then the distribution of the measurements is flatter than the true distribution. The variance of a measured variable is the sum of the true variance and the measurement error variance. If we shrink measured values towards their mean so that the variance will be equal to the true population variance, or its estimate, the obtained empirical distribution is more similar to the true distribution than is the distribution of measured values. To estimate the population variance, an estimate of the variance of measurement errors is required. If stand densities are measured by counting trees on fixed area or angle gauge plots, then a first approximation for the measurement (sampling) error variance can be computed assuming random (Poisson) spatial pattern of trees. The suggested estimation method is illustrated using an assumed distribution of stand densities.