Best functional form to describe a scatterplot with a z-shape appearance with noise

What might be the general form of the equation can be fitted to the below scatter plot? The result should look like an smooth Z

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is there any reason why some observations are dots and other crosses? --otherwise, i would say a complementary log-log function (after appropriately re-scaling the vertical axis to get things in 0-1), because of the strong assymetry [you will find it in R in the VGAM library, function cloglog()] –  user603 Aug 8 '11 at 10:05
the plot includes two time series, one showed by empty disks and the other by crosses. I prefer to keep the vertical axis in linear form and not to change it into logarithmic scale. –  K-1 Aug 8 '11 at 10:45
The hyperbolic tan (tanh) has a z-shape with bounds -1..1 for y. You might try this using appropriate shift and scaling of the x and y-values –  Gottfried Helms Aug 8 '11 at 10:59
@Gottfried Helms; sure but that's just still one form of log transform ( stats.stackexchange.com/questions/1444/… ) –  user603 Aug 8 '11 at 11:03
This shape is called sigmoid. –  mbq Aug 8 '11 at 11:05
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then, you might want to try additive models for quantile regressions (some pics/explanation here, and the $\verb+R+$ implementation here). These have various desirable properties:
2. They are robust to outliers on $y|X$, and judging by the plot, you seem to have of those aplenty.