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With the help of @JimB, I could fit some experimental data with a CDF using NonLinearFitModel. The set of data is the following:

data ={{0.995, 0.142}, {3.003, 0.2}, {5.908, 0.25}, {10.525, 0.36}, {13.617,
   0.498}, {24.321, 0.616}, {33.917, 0.599}, {47.843, 0.7}, {64.172, 
  0.835}, {91.353, 1.102}, {126.745, 1.083}, {174.118, 
  1.225}, {225.059, 1.133}, {292.998, 1.165}, {369.133, 
  1.298}, {640.295, 1.365}, {828.169, 1.298}, {1255.39, 
  1.373}, {1496.61, 1.409}, {1942.79, 1.538}} 

and the suggestion of @JimB for the best fitting was

nlm = NonlinearModelFit[data, b CDF[NormalDistribution[c, d], Log10[t]], {b, c, d}, t];

rateOfChange = D[nlm[10^log10t], log10t] /. 10^log10t -> t

The final result of the analysis is the following plot, with the inset being the derivative (rate of change) of nlm: enter image description here

Given that the best fit was performed using a CDF, I'd like to know if:

Instead of calculating the rate of change through the derivative, is it possible the obtain directly a PDF which enables me to construct a histogram?

Thanks in advance and sorry to continuosly post similar questions here.. I'm some kind of desperate :(

PS.: References of statistical analysis, fitting experimental data with distribution and related thinks would be welcome. I'm a beginner with WM and any suggestion would be helpful

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    $\begingroup$ I welcome to become enlightened if I'm wrong but I think attempting to construct a "histogram" (which is really a bar chart in this case as there are no "counts") would be a step backwards. The data you have is used to estimate a cumulative function (not a CDF) and you have the derivative of that function which is the underlying object you're trying to estimate with the data. $\endgroup$ – JimB May 3 at 22:13
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    $\begingroup$ As I understood, you can obtain the featured CDF if you know the fitted parameters b, c and d? They are available from nlm["BestFitParameters"] $\endgroup$ – Rom38 May 4 at 5:53

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