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    $\begingroup$ The Jacobian contains Log[x] and your data contains x == 0 $\endgroup$ Commented Jan 28, 2019 at 17:09
  • $\begingroup$ @Coolwater: There are other methods of fitting. $\endgroup$ Commented Jan 28, 2019 at 17:43
  • $\begingroup$ It's all about providing good starting values when there are 7 parameters (a, b, c, d, e, and the error variance) to estimate with only 18 (or 17 legitimate) limited precision data points. Following @Coolwater 's approach gets you good starting values for use in NonlinearModelFit. $\endgroup$ Commented Jan 28, 2019 at 18:31
  • $\begingroup$ @JimB: I tried you advice, obtaining "NonlinearModelFit::nrjnum: The Jacobian is not a matrix of real numbers at {a,b,c,d,e} = {2.75699,1.66039,2.92883,4.74005,0.70619}.". $\endgroup$ Commented Jan 28, 2019 at 18:37
  • $\begingroup$ Drop the observation with x=0 and it will work just fine. $\endgroup$ Commented Jan 28, 2019 at 18:38