# Dictionary:Sech criterion

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(sek) An optimization criterion involving minimizing

${\displaystyle \sum {\text{ln}}\left[cosh\left[{\frac {\left(d_{i}^{\star }-d_{i}\right)}{\sigma }}\right]^{2}\right]}$,

where ${\displaystyle d_{i}^{\star }}$ are observed and di are model data. Implies that errors have the probability distribution ${\displaystyle {\frac {1}{\pi \sigma }}sech\left[{\frac {\left(d-d_{0}\right)}{\sigma }}\right]}$, where sech is the hyperbolic secant and ${\displaystyle \sigma }$ is the standard deviation about the maximum likelihood point d0.