THE EGS5 CODE SYSTEM

Figure 2.6: Plots of Molière functions f (0) , f (1) , and f (2) .
and thus, are not candidate distribution functions. Graphs of f (1) (θ) and f (2) (θ) are shown in
Figure 2.6. We now adopt a strategy similar to that used by Messel and Crawford[103]; namely,
mix enough of f (0) (θ) with f (1) (θ) and f (2) (θ) to make them everywhere positive. Unlike Messel
and Crawford, who dropped the term involving f (2) (θ), we have been able to retain all of the first
three terms in the expansion.
where
The factorization we use is
3∑
f r (θ) = α i f i (θ)g i (θ) , (2.328)
i=1
α 1 = 1 − λ/B , (2.329)
g 2 (θ) =
f 1 (θ) = 2e −θ2 θ for θɛ(0, ∞) , (2.330)
g 1 (θ) = 1 , (2.331)
α 2 = µg 2,Norm /B , (2.332)
f 2 (θ) = 1/µ for θɛ(0, µ) , (2.333)
θ (
)
λf (0) (θ) + f (1) (θ) + f (2) (θ)/B , (2.334)
g 2,Norm
α 3 = g 3,Norm /2µ 2 B , (2.335)
f 3 (θ) = 2µ 2 θ −3 for θɛ(µ, ∞) , (2.336)
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