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I have experimental data points that can be modeled by two different rational polynomials.

I am wondering if there is a way (e.g. by a transform or integral), to discriminate the following two rational polynomials (defined for $x\in\mathcal{R}^+$):

$$f_1(x)=\frac{a+bx^2}{c+dx^2}$$

and

$$f_2(x)=\frac{d+ex^2+fx^4}{g+hx^2+lx^4}$$

where $a,b,c,d,e,f,g,h,l>0$.

Any suggestion?

JFNJr
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  • You want to tell whether your data is better fit by one than the other? – MichaelChirico Jun 23 '15 at 17:12
  • @MichaelChirico Actually I would like to find a way not to fit the data and then compare the goodness of fit. For instance, the Inverse Laplace transform of those functions gives two functions with completely different behavior for $x\to \infty$, but the ILT is not numerically feasible. Is it now clearer what I am looking for? – JFNJr Jun 23 '15 at 17:15
  • Not exactly; please ellaborate – MichaelChirico Jun 23 '15 at 17:16
  • @MichaelChirico Probably I need an integration with some special function (e.g. Bessel functions) that can give different results because of the different degree of rational polynomials. – JFNJr Jun 23 '15 at 17:18
  • Still lost. Could you add some context on what exactly your problem is and what you'd like to accomplish? Also, perhaps this is better suited to Cross Validated – MichaelChirico Jun 23 '15 at 17:20
  • Hmm, I'm wondering...by $x \in \mathcal{R}^{+}$ do you really mean $x \in \mathbb{R}^{+}$ or something else? – Obinna Nwakwue Aug 12 '16 at 21:10

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