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  • $\begingroup$ Just a point of clarification: You are estimating a curve that has the same shape as a Gaussian distribution as opposed to estimating a Gaussian probability density (or CDF) from a random sample. In other words you are performing a regression and the procedures (Gaussian Mixture Model and maximum likelihood estimation from a random sample) associated with estimating the parameters do not apply. $\endgroup$ Commented Jul 25, 2019 at 16:11
  • $\begingroup$ Why not just replace ` b CDF[NormalDistribution[c, d]` with ` b1 CDF[NormalDistribution[c1, d1] + b2 CDF[NormalDistribution[c2, d2]` ? Providing example data would be helpful to provide specific advice. $\endgroup$ Commented Jul 25, 2019 at 16:12
  • $\begingroup$ The data size 20 is too small to make reliable conclusions. Statistics begins from 30 (see google.com.ua/… ). $\endgroup$ Commented Jul 25, 2019 at 16:32
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    $\begingroup$ @user64494 Have you read very many of the search results? There is no minimum sample size that applies to some applications of some fields of study even some of the time. A sample of size 2 is a valid sample size. Whether any sample size is adequate (as opposed to "valid") depends on the variability of the samples, objectives of the study, desired levels of precision, how well various assumptions hold, etc. In this forum I have complained multiple times when someone wants to fit a fifth-degree polynomial with just six data points. In short, "It depends." $\endgroup$ Commented Jul 25, 2019 at 17:04
  • $\begingroup$ @JimB, Thanks for the feedback and for the clarification. And yes, what I'm trying to do is to perform a regression and the reason for my insistence in trying to relate this best fit with a CDF is that I want to associate this measured data with a (supposed) random variable that can be described in terms of a probabilistic distribution. In order words, the shape of this curve (which in my approach looks like a -or a set of- CDFs) can be interpreted as a result of the presence of one or more different PDFs. $\endgroup$ Commented Jul 25, 2019 at 17:47