Setting Data Distribution - MATLAB

Question

I am trying to fit the distribution to some data that I have collected from microscopy images. We know that the peak at about 152 is due to the Poisson process. I would like to place the distribution at a higher density in the center of the image, ignoring the high-intensity data. I know how to fit the normal data distribution (red curve), but it does not do a good job of capturing the heavy tail on the right. Although the Poisson distribution should be able to model the tail to the right, it does not do a very good job (green curve), because the distribution mode is 152.

PD = fitdist(data, 'poisson'); 

The Poisson distribution with lambda = 152 looks very Gaussian.

Does anyone have an idea how to fit a distribution that does a good job of capturing the right tail of the data?

Link to an image showing the data and my attempts to set up a distribution.

Answer 1

The distribution looks a bit like Ex-Gaussian (see the green line in the first Wikipedia figure), i.e. a model of a mixture of normal and exponential random variables.

On the side of the note, did you know that although the events of the Poisson process are distributed over the Poisson, the waiting time between the events is exponentially distributed? Given that Gaussian noise has been added to your measurements, you could theoretically use ex-Gaussian propagation. (Of course, this does not mean that it is also believable.)

Ex-gaussian installation tutorial with MatLab can be found in

Lacouture Y, Cousineau D. (2008) How to use MATLAB to match ex-Gaussian and other probability functions to distribute response times. Textbooks on quantitative methods of psychology 4 (1), p. 35-45. http://www.tqmp.org/Content/vol04-1/p035/p035.pdf

Answer 2

take a look at this: http://blogs.mathworks.com/pick/2012/02/10/finding-the-best/

he discusses the following FEX view of installation distributions: http://www.mathworks.com/matlabcentral/fileexchange/34943