Fitting a gamma distribition to x,y data

Dear all,

i do have data from size distribution measurements. The data is like: number of counts in specific size class ( e.g 1 - 1000 µm).

I can use nlinfit like:

p = nlinfit(sizeclass,NormalisedCounts,@gammafun_3param,[1 10 1500])

with

function y = gammafun_3param(abc,x)
a = abc(1); b = abc(2); c = abc(3);
y = c * x.^(a-1) .* exp(-x/b) / (b^a * gamma(a));
end

This works pretty well. The reason why i do not understand this issue is probably due to my lack of statistic knowledge.

1) Why does the usual gammafunction with c=1 not fit (the scaling is wrong)

2) How can i use gamfit if i cannot pass the information of the sizeclass to it ?

Do i have to normalize the data somehow different ? I normalized the counts by dividing by their sum.

Kind regards

Moritz