Probable limit of error of the point distance-neighbour distance estimate of density

A formula is proposed for calculating the probable limit of error (PLE) of the density estimate which is obtained from measurements of distance from sample points to the nearest member, its nearest neighbour, and its nearest neighbour.
It takes the form:
PLE = tÃD / √N,(where t is Student's t, Ã is a measure of non-randomness, D is the estimate of density, and N is the number of sample points) and is considered to be analogous to the usual bounded plot sampling error formula tS / √N for the specific case where density averages one per plot. Using Student's t for the 95 percent level of probability, 90 percent of the density estimates, drawn from 40 computer-simulated populations were within the ranges given by the proposed formula. Similarly, 92 percent of 36 estimates obtained from 11 paper-dot populations and 76 percent of 93 estimates obtained from 25 natural populations were within the proposed PLE. In some of the remaining cases, the extent by which the proposed PLE's were less than the calculated difference between true density and D were quite trivial. Some anomalies probably arose from sampling difficulties