[Akaike's information criterion](http://en.wikipedia.org/wiki/Akaike_information_criterion) is a measure of the goodness of fit of an estimated statistical model that accounts for both the fit quality and model complexity. One way to calculate AIC is as follows:


$\mathit{AIC}=2k + n[\ln(\mathit{RSS})]\,$


, where $k$ is the number of parameters in the model and $\mathit{RSS}$ is the residual sum of squares.


Assume two models:


$f\_1(x) = ax$


and


$f\_2(x) = \frac{ax}{b + cx} + d \sin(x)$


.
Is the number of parameters, $k$, in both the models equal 1?


**EDIT** In the equations above only $x$ is a variable, while $a$, $b$, $c$ ... are constant parameters



Number of parameters in Akaike's information criterion
The question should be: how many of the parameters need to get estimated based on the data? If three of them were somehow known independently of the data, then I say for present purposes there's only one.


The nonlinearity in $x$ in the $\sin x$ term is not a concern because $f\_2(x)$ is linear in $\sin x$ and the parameter is multiplied by that. But I'm wondering whether fitting by minimizing the residual sum of square makes sense when you have nonlinearity in $x$ in the other term.


Akaike's information criterion is one of many used for this purpose that I've heard of, and I'm really not familiar with any of them except to a minor extent that of Mallows.


