How to fit a histogram plot to a poisson distribution

I have a histogram plot which looks like this. where I have only plotted spacing_ratios = diff(energies) ./ mean(diff(energies)). energies corresponds to the eigenvalues of a particular hamiltonian matrix. I have used the code

edges=linspace(min(spacing_ratios),max(spacing_ratios),300);

h=histogram(spacing_ratios,'BinEdges',edges);

Now I want to fit this histogram plot to poisson distribution such that the probabilty of having n energy levels in a particular interval of energies E and E+deltaE will be

where \lambda is the average number of levels in that interval. How can I fit this with my numerical results shown above?

[the cyclist]

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[Abhik]

Please see the attached data. note that i have not normalized the data this data is the raw data

[Torsten]

Do you have an additional question ? I think your original question has been answered, hasn't it ?

[Abhik]

using poissfit I can not fit the data I also do not know how to scale the histogram plot because what i am getting is the raw data of energy spacing Now I want a plot that describe this raw data with proper scaling so that I can get the unknown parameter of the poisson distribution

[Torsten]

Your data contain non-integer values - so they cannot follow a Poisson distribution.

To fit a distribution, you usually do not scale the data - you work with the raw data.

To get an empirical distribution curve for your data, use

histogram(spacing_ratios,'Normalization','pdf')

Answer 1

[Torsten]

Simply use

lambdahat = poissfit(spacing_ratios)

But I'm surprised you want to fit data that take non-integer values with a distribution that has only mass on the set of the natural numbers. Isn't that inadequate ?

[the cyclist]

I agree, and frankly I'm surprised that poissfit doesn't give a warning for non-integer input. (Maybe I'm forgetting something.)

Perhaps wblfit is more appropriate (applied to the original data, not the histogrammed data, as @Torsten did in this solution). But, of course, the correct distribution to use depends on the underlying distribution that is theorized to have generated the data.