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The corrected Akaike information criterion adds a finite-sample penalty to the Akaike information criterion, where $k$ counts fitted parameters and $n>k+1$. The displayed correction is commonly used for small samples; its exact unbiasedness depends on the model family.

Both candidate models fit one parameter, but their parameter symbols have different meanings. For the exponential distribution in model B,Its second derivative is $-N/{\theta }_B^2<0$, so this is its maximum-likelihood estimate. The maximized log-likelihoods, including their normalization terms, areUse the corrected Akaike information criterion because $N=4$ is small relative to the number $k=1$ of fitted parameters:The correction is $2$ for each model, givingPrefer model A, whose corrected Akaike information criterion is smaller by $7.67252$. The ordinary Akaike information criterion also gives that ranking because the two models receive equal penalties. This compares the two proposed models; it does not establish that either is a correct description of the process. The usual corrected Akaike information criterion formula is a small-sample model-selection convention, rather than an exact finite-sample guarantee for these density families.