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I need to fit a cumulative distribution that is monotonically decreasing. I have in mind to use a polynomial of the lowest order that will give a fit that is looks good to the eye. Can someone suggest a polynomial functional form that is monotonically decreasing?

jhadams1
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  • over what domain? – bubba Mar 11 '13 at 13:09
  • Cumulative distribution functions tend to be increasing. – Eckhard Mar 11 '13 at 13:19
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    Either use a polynomial in e.g. $e^{-z}$ or a rational function. Plain polynomials don't have asymptotes (and a cumulative distribution does $\rightarrow 1$ as $z \rightarrow \infty$). I.e., get the overall form right and then adjust parameters. – vonbrand Mar 11 '13 at 13:56

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While polynomials can be decreasing or increasing (e.g., $f(x)=-x$ or $f(x)=x^3$), they cannot have a finite limit as $x\to\infty$ (except by being a constant function). Both suggestions by vonbrand are very good: use a polynomial of $e^{-x}$ or a rational function of $x$. Lacking further information, I would go with the polynomial of $e^{-x}$ (or a similar decaying function), because in this case we get a linear system of equations for coefficients, when fitting the curve using least squares method.

ˈjuː.zɚ79365
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