N. Van Der Hoeven, Estimating the 5-percentile of the species sensitivity distributions without any assumptions about the distribution, ECOTOXICOL, 10(1), 2001, pp. 25-34
A non-parametric method is described to estimate the hazardeous concentrati
on for p% of the species, the HCp, and the confidence limits for this value
, the HCp(alpha). For this method, all observed sensitivities are ordered f
rom high to low sensitivity. The HC5 is the k-th observation were k is the
largest integer below 0.05 x (n + 1). It is described how the HCp(alpha) ca
n be calculated. A table is presented for easy calculation of several conse
rvative confidence limits for the HC5. For the HC5(0.05), a second table is
presented which can be used to interpolate between the conservative estima
te of the HC5(0.05) and the next higher observed concentration. The non-par
ametric HC5 and HC5(0.05) estimation is illustrated with an example of sens
itivity data on malathion. For this data set, the log-normal HC5 and HC5(0.
05) estimations appear to be conservative compared with the non-parametric
estimate. It is stressed that HC5 and HC5(0.05) estimates will often be muc
h more affected by the non-randomness of the species set for which sensitiv
ity data are available than by the choice of the statistical method.