Why do I get different lognormal parameters using lognfit vs. using the fit function with the lognormal equation?

I am working to fit a lognormal distribution to in situ aerosol size distribution data. I have tried a variety of approaches. When I use lognfit or calculate mu and sigma by hand (calculating the mean and standard deviation of the natural log of the data), I get the same numbers (mu = -10.3954, sigma = 1.8503). However, the PDFs based on these values do not match the data at all. In the plot below, the blue represents the mu and sigma when I use lognfit or calculate by hand, and orange is my actual data.

I have also tried using the MATLAB "fit" function with a specified (lognormal) equation and initial guesses for the parameters. When I use this method, I get mu and sigma values that make more sense when looking at the data (mu = -1.8843, sigma = 0.3915). Below I show this lognormal pdf compared to the data.

I have been trying to reconcile the differences between these methods for days and can't seem to figure out anything that makes sense. In short, I am wondering why these methods are giving such different answers? Any help would be appreciated!

Answer 1

[Torsten]

Does this help ?

https://uk.mathworks.com/matlabcentral/answers/2067676-lognormal-fitting-with-the-pore-size-and-its-probabilities?s_tid=srchtitle