Question

I have been looking around for a while on fitting Levy Distributions to a histogram to no avail. I am hoping to test out how a Levy Flight distribution would look on the data regardless of whether it truly is the right fit for our data type. Since I am rather new at PDFs and fitting my own PDFS aside from the distfittool GUI in matlab, I am a bit unaware of what I need to do to properly do this.

So currently, my data is a 208×1 vector, 208 points represents different speeds for 208 distinct objects. Speeds were calculated just via overall distance per time.

Now, currently I took the function that describes the Levy flight from:
http://reference.wolfram.com/mathematica/ref/LevyDistribution.html (Out[3])

And I used the following code to try it out:

load('Speeds.mat')
modelFun = @(p,x) (exp(-p(1)./(2.*(x-p(2)))).*(p(1)./(x-p(2))).^3/2)./(sqrt(2.*pi).*p(1));
startingVals = [1 1];
coefEsts = nlinfit(LBSpeed,modelFun,startingVals);

I am completely aware that my lack of familiarity with the Levy flight distribution is the root of why I am not even sure whether that is the proper function to use for the distribution, nor the arguments I need to pass to it to properly do this. If anyone could give me a bit more insight, I’d greatly appreciate it.

Answer 1

I have seen similar questions to this problem with no answers, so after getting help from a colleague I wanted to post the solution

The other thing that was changed from my original question, is that it became piecewise to better satisfy the reference of the levy flight equation I posted myself. The starting vals I chose were arbitrary.

load('Speeds.mat')
[N,X] = hist(Speed,20);
Y = N/(sum(N))/diff(X(1:2));

%Get best parameters
modelFun = @(p,x) (x>p(2)).*(exp(-p(1)./(2.*(x-p(2)))).*(p(1)./(x-p(2))).^(3/2))./(sqrt(2.*pi).*p(1));
startingVals = [1,1];
coefEsts = nlinfit(X,Y,modelFun, startingVals);

%Visualize fit
bar(X,Y);
hold on;
model_eval = modelFun(coefEsts,X);
plot(X,model_eval,'r','LineWidth',2);

I wasn’t aware of how to fit histograms in the first place, so hope this helps someone new to this!