Prediction of tree-size distributions and inventory variables from cumulants of canopy height distributions

The method of predicting an unknown target probability distribution via a Gram– Charlier A-series expansion (GCAE) of a user-defined base probability function and cumulants of a known distribution of an auxiliary variable is demonstrated in two applications. Both applications concern predictions of the distribution of tree stem diameters with cumulants of airborne laser scanning (ALS) canopy heights and an index of canopy density as predictors. All predictions were generated in a leave-one-out cross-validation scheme, and statistical inference was based on 100 stochastic predictions of the tree sizes in 308 plots of 400 m 2 . The mean and variance of GCAE-predicted distributions were rarely significantly different from actual values, yet between 19 and 32% of the predicted GCAE distributions were significantly different from the actual distribution. The rejection rate with predictions generated from a simpler DECILE method was, on average, 2.5% lower. GCAE is still recommended due to its potential usefulness. Cumulants of ALS canopy heights are independent of plot area and effective for area-based leastsquares predictions of forest inventory variables.