Environmental Decision-Making - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 228

Fig. 3.4 Response of the
density of the Wald ' s
distribution function to the
variations of parameter c

Z

x

W c ð x Þ ¼ w c ð z Þ dz ; ð 3 : 12 Þ

0

)] − 1 .
The universality of the distribution ( 3.12 ) follows from its duality to the
Gaussian distribution. As far back as 1960 Wald showed that if E a n

) 1/2 z − 3/2 exp[ 0.5c(z+z − 1 )] 2 [D(

where w c (z)=(c/2 ˀ − − 2)] and c =[E( m m

j j and D a n are

suf ned by

the expression ( 3.11 ) will be a close approximation to the real one even for

ciently small in comparison to lnA and lnB, the distribution of m /E a m de

n not

distributed by the Gaussian law.
Theoretical aspects of the universality of the distribution W c (x) are important for
the integrated estimation of the sequential procedure ef ciency. However, these are

not the principal aspects for experimental applications. For that reason, as a rule, the
synthesis of the decision making system is perceived without these considerations.
In fact, the volume of the measurements, as a rule, is small and the central limit
theorem doesn

culties arising from this can be overcome
by evolutionary modeling (Bukatova et al. 1991), intelligent technology (Nitu et al.
2000b) and the use of other algorithms.

' t work. The statistical dif

3.3 Decision-Making Procedure Using the Sequential
Analysis

In contradiction to the Neyman-Pearson criterion (Yan and Blum 2001), the

sequential procedure doesn t separate the stages of measurement and data processing

but it alternates them. This is represented schematically in Fig. 3.2 incomparison to

'