# Dictionary:Cauchy criterion

${\displaystyle \sum ln\left\{1+\left[{\frac {d_{i}^{\star }-d_{i}}{\sigma }}\right]^{2}\right\}}$ ,
where ${\displaystyle d_{i}^{\star }}$ are observed and ${\displaystyle d_{i}}$ are model data. Implies that errors have the probability distribution
${\displaystyle {\frac {1}{\pi \sigma }}\left\{{\frac {1}{1+\left[{\frac {d-d_{0}}{\sigma }}\right]^{2}}}\right\}}$,
where ${\displaystyle \sigma }$ is the standard deviation about the maximum likelihood point d0. See Amundsen (1991, 2027).