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Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / General<br />

_ _<br />

C<br />

: =<br />

A + S<br />

i + 1<br />

⋅<br />

22.2-7<br />

4.<br />

656613x10<br />

−10<br />

⋅<br />

( B − A )<br />

The uniformly distributed variable (C) is taken from the <strong>pdf</strong>,<br />

C<br />

∈<br />

[ ] ( ) ( ) 1 −<br />

A,<br />

B ⇒ p C : = B − A<br />

[ A , B ] ⇒ p ( C ) : 0<br />

C ∉<br />

=<br />

Equation 22.2-40<br />

Equation 22.2-41<br />

Equation 22.2-42<br />

UNIFORM generates random numbers using integer overflow and must be<br />

compiled without overflow checking. If (AB) a fault report is written to the<br />

ASCII output file (channel LUNOUT) and the simulation is terminated.<br />

22.2.4.5 Rayleigh Distributed Variables<br />

When (M := 2) RANDOM uses RAYLEIGH to return a Rayleigh distributed<br />

random variable (C) defined by (A), (B) is not used, whilst updating seed<br />

IRAND(N).<br />

RAYLEIGH ( IRAND(N) , A , C )<br />

Equation 22.2-43<br />

RAYLEIGH invokes UNIFORM to update the seed and provide a uniformly<br />

distributed random variable in the range [10 -15 ,1-10 -15 ], denoted in the<br />

following equations by U[0,1] for convenience, transformed into a Rayleigh<br />

distributed random variable,<br />

C : = − 2 ⋅ ln<br />

( U [ 0,<br />

1 ] )<br />

The Rayleigh distributed variable (C) is taken from the <strong>pdf</strong>,<br />

( ) ⎟ ⎛ 2<br />

C C ⎞<br />

C > 0 ⇒ p C : = ⋅ exp ⎜<br />

−<br />

2<br />

2<br />

A ⎝ 2 ⋅ A ⎠<br />

( C ) : 0<br />

C ≤ 0 ⇒ p =<br />

Equation 22.2-44<br />

Equation 22.2-45<br />

Equation 22.2-46

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