Finney minimum variance unbiased estimator described by Aitcheson and
Brown.24

The Krige method using 4 minimum variance unbiased estimator

is optimal under the assumption of lognormal distribution (Aitchison and
Brown 34 p- 44).

The shift parameter, tT, is calculated using Krige's

quantile formula.??

The tT is involved in the log-transform as log

(x, -T), where X; are measurement values in pCi/gm and may be
negative and below the minimum detectable activity (MDA).

The

param-

eter removes problems of taking logrithms of negative numbers and improves
the approximation to the lognormal probability density function.
computer algorithm calculates the first T.

Figure 8,

The

T = 0.6 pCi/cn,

exhibits an example where the left MDA concentrations are forced more
closely to a straight line than the same data with T = o (Fig. 7) using
the Krige method?? to adjust this parameter about the first approximation to maximize the r-test value.

The means and variances arc

calculated using the Finney fifteen term eapproximetion to 4 mininun
variance estimate (Aitchison and Brown, 24 Eq.

5.37).

A visual inspec-

tion of each data set is done by a log-probability plot (examples on
Figs. 4 to 10).

For comparison,

using the quantile method.2*

the mean and variance was estimated

The minimus variance log-probability-line

was used to find the quantile values.

Numerical approximations to the

cumulative normai distribution used formulas 26.2.23 and 26.2.22 in
Abromowitz and Stegun's handboc::.49
the comparison of methods

Tables 45 through 47 illustrate

for 24) bry which have severa]

and 137¢5 at the same sample location.

For 24. an,

censored values,

the arithmetic

mean frequently underestimates the Krige method (average of 30 percent,

, underestimation range: 0 to -100 percent, 0-15 cm soils), but the

40 -

a

so11114

Select target paragraph3