A fixed count sampling estimator of stem density based on a survival function

In fixed count sampling (FCS) a fixed number (k) of observations is made at n randomly selected sample locations. For estimation of stem density, the distance from a random sample location to the k nearest trees was measured. It is known that practical FCS estimators of stem density are biased. With the objective of reducing bias in FCS estimators of stem density, a new estimator derived from a survival function with distance acting as time was presented. To allow for spatial heterogeneity in stem density, the survival function includes shared frailty. Encouraging results with k = 6 in terms of bias, root mean squared error (RMSE), and coverage of nominal 95% confidence intervals were obtained in an extensive testing with simulated random sampling from 54 actual and four simulated spatial point patterns of tree locations. Sample sizes were 9, 15, and 30, with 1200 replications per setting. The performance across sites of the new FCS estimator was variable but almost paralleled that of a design-based estimator with fixed area plots. Users of the new FCS estimator can expect an absolute relative bias and a root mean squared error that are 1% greater than for sampling with fixed area plots holding an average of k trees. The chance of a smaller RMSE with the proposed estimator was estimated at 0.44.