Dictionary:Cauchy criterion

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{{#category_index:C|Cauchy criterion}} (kō shē’) An optimization criterion involving the minimizing of

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \sum ln \left\{1+\left[ \frac{ d^\star_i - d_i } {\sigma}\right]^2\right\} } ,

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle d^\star_i} are observed and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle d_i} are model data. Implies that errors have the probability distribution

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{1}{\pi\sigma}\left\{ \frac {1}{1+\left[\frac{d-d_0}{\sigma}\right]^2}\right\}} ,

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \sigma } is the standard deviation about the maximum likelihood point d0. See Amundsen (1991, 2027).