this is for holding javascript data
Matt Pitkin edited As_can_be_seen_in__.tex
over 8 years ago
Commit id: fc7a74d969e8ac6dde488493305b28536f94e35d
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As can be seen in Figure~\ref{fig:fermidirac} the probability falls to 50\% of the maximum at $\mu$. The width of the attenuation of the probability is defined by the $\sigma$ value, such that smaller $\sigma$ values mean that the probability falls off more quickly (still centred on $\mu$). If we say that
$r=\mu/\sigma$ $r=\mu/\sigma$, and decide to define the distribution in terms of $\mu$ and $r$, then we can empirically estimate the attenuation band as a function of
this parameter. these parameters. The band over which the probability falls from 97.5\% of the maximum value down to 2.5\% is given by $\mu \pm
Zr\sigma^2/2$, Z\mu^2/2r$, where $Z \approx 3.345$.