# What equation best formalizing a S shaped curve with long flat linear part in the middle with strong slope

I'm searching for a type of equation describing best a S-shaped curve with a quite long flat linear part in the middle with strong slope.

Here are numerical example:

x_data = [0,    0.1,    0.2,    0.3,    0.4,    0.5,    0.6,    0.7,    0.8,    0.9,    1]
y_data = [15.61,    7.02,   5.87,   5.17,   4.69,   4.21,   3.77,   3.32,   2.85,   2.24,      0.16]


I tried 3rd polynom [$y=a.x^3+b.x^2+c.x+d$], general S-shaped curves [$y=a / (b + e^{(c*x+d)})$] but both fail to describe this long flat linear part in the middle with hard slope. The very pedagogic answer from joriki helped me a lot, indicating an equation like $y=\frac1{1+\mathrm e^{B_1-x}}+\frac1{1+\mathrm e^{B_2-x}}\;$, but it still misses the long slope of the flat linear part in the middle I have in my numerical example. What kind of curves family or equation may help me describing this curve with long flat linear part in the middle with strong slope? Thanks for incoming help.

• Try using $[x,y+3.6x-5.5]$ which looks like exponential decay except near the end. Commented Apr 20, 2018 at 15:03
• Sorry Somos I don't understand your proposal :-S
– sol
Commented Apr 20, 2018 at 17:16
• I meant use the original x_data and then y_data+3.6*x_data-5.5 instead of original y_data. Commented Apr 20, 2018 at 17:38