Here is the data that I used to get this plot:
{0., 2.61706*10^-15, 6.94662*10^-9,
1.27056*10^-6, 0.0000197033, 0.000110735, 0.000369473, 0.000907843,
0.00183323, 0.00323707, 0.00519123, 0.00774869, 0.0109459, 0.0148059,
0.0193404, 0.0245531, 0.0304405, 0.0369943, 0.0442024, 0.0520496,
0.0605186, 0.0695905, 0.0792451, 0.0894615, 0.100218, 0.111494,
0.123266, 0.135513, 0.148212, 0.161342, 0.174881, 0.188807, 0.203099,
0.217736, 0.232697, 0.247961, 0.263508, 0.279318, 0.295372, 0.311648,
0.328129, 0.344794, 0.361624, 0.378602, 0.395708, 0.412923, 0.430229,
0.447608, 0.465042, 0.482512, 0.5, 0.517488, 0.534958, 0.552392,
0.569771, 0.587077, 0.604292, 0.621398, 0.638376, 0.655206, 0.671871,
0.688352, 0.704628, 0.720682, 0.736492, 0.752039, 0.767303, 0.782264,
0.796901, 0.811193, 0.825119, 0.838658, 0.851788, 0.864487, 0.876734,
0.888506, 0.899782, 0.910538, 0.920755, 0.93041, 0.939481, 0.94795,
0.955798, 0.963006, 0.96956, 0.975447, 0.98066, 0.985194, 0.989054,
0.992251, 0.994809, 0.996763, 0.998167, 0.999092, 0.999631, 0.999889,
0.99998, 0.999999, 1., 1., 1.}
I've tried using the Fit[] function (as well as several other similar ones, such as FindFit[], NonlinearModelFit[], etc.). The function FindFormula[] also doesn't seem to be working for me.
This data was obtained from the answer to another question I asked here: Mathematica won't evaluate this integral (thanks to user @rmw for pointing out that I should include this).
Many thanks.
d=Differences[data]; ListPlot[d]
. $\endgroup$ – JimB May 9 '19 at 14:10