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@Carl your suggestion was quite useful and it worked for me. can you please suggest some reading for the algorithm behind it? I would like to replicate it in python. whuber thank you for your comment I havent gotten around it yet, will try and update.
I guess I am bit inexperienced to convey properly, histogram is the observed size distribution of particles. I would like to model the observed data as noise from the instrument (Exponential distribution as noise is most likely to be small specs and static etc.) + log normal distribution of particles . After thinking over it more I got one problem in my approach that I need the function to model the data with input noise source. I am trying to model the data as sum of random distributions. I am just little confused as how to proceed next