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pastas.stats.metrics.aicc#

aicc(obs=None, sim=None, res=None, missing='drop', nparam=1)[source]#

Compute the Akaike Information Criterium with second order bias correction for the number of observations (AICc)

Parameters
  • obs (pandas.Series, optional) – Series with the observed values.

  • sim (pandas.Series, optional) – The Series with the simulated values.

  • res (pandas.Series, optional) – The Series with the residual values. If time series for the residuals are provided, the sim and obs arguments are ignored. Note that the residuals must be computed as obs - sim here.

  • nparam (int, optional) – number of calibrated parameters.

  • missing (str, optional) – string with the rule to deal with missing values. Only “drop” is supported now.

Return type

float

Notes

The corrected Akaike Information Criterium (AICc) [] is computed as follows:

\[\text{AIC} = -2 log(L) + 2 nparam - (2 nparam (nparam + 1) / (nobs - nparam - 1))\]

where \(n_{param}\) is the number of calibration parameters, nobs is the number of observations and L is the likelihood function for the model. In the case of ordinary least squares:

\[log(L) = - (nobs / 2) * log(RSS / -nobs)\]

where RSS denotes the residual sum of squares.