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MLDK2SIM

The MLDK2SIM program, for the CONVEX, performs Monte Carlo trials of dimension and entropy estimates. These are estimated using distances drawn from the proposed distribution. This is done using the NAG [Numerical Algorithms Group, 1983] random number generator. The routine G05CCF puts the generator in a non-repeatable state using the system clock (8640000 different states). Uniformly distributed noise $[0,1]$ is then obtained with
\begin{displaymath}
x = \mbox{G05CAF()}
\end{displaymath} (5.75)

so
\begin{displaymath}
r = {\left( \frac{x}{\phi} \right)}^{\frac{1}{\nu}}
\end{displaymath} (5.76)

is distributed as desired since (see also [Hogg and Craig, 1978, p.127])
\begin{displaymath}
1.dx = 1.d\phi r^{\nu} = \phi\nu r^{\nu-1}dr
\end{displaymath} (5.77)

$N$ distances are drawn, and the numbers $N_{l}$, $N_{s}$ and $\sum \ln \left( \frac{r}{r_{u}} \right) $ determined. This is done for two values of $\phi$; they are computed from the specified entropy, time delay, embedding dimension and offset $e$. The ``single'' and ``double'' dimensions and entropies are estimated. After repeating this procedure, sample means and variances are estimated together with confidence intervals. The value of $Z_{\alpha/2}$ in eq. (5.69) is computed using NAG routine G01CEF. The variances are multiplied by $N$ so that these quantities should converge to a constant value, i.e. the Cramér-Rao lower bound times $N$ (Eqs (5.37), (5.53) and (5.55)).


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