CDF and Inverse CDF of Wrapped Cauchy Distribution

wasim shaikh - 2022-04-14T11:23:12+00:00

Question: CDF and Inverse CDF of Wrapped Cauchy Distribution

The standard wrapped-up Cauchy distribution has the following probability density function:   f(x,p)= {1-p^2}/{2*pi(1+p^2-2*p*cos(x)}, Where x is from 0 to 2*pi   Follow this link for the mathematical expression: Wrapped Cauchy Distribution PDF   What is the CDF and INVCDF of this probability distribution? Any command or code is available in MATLAB to get INVCDF?

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Expert Answer

John Williams answered . 2025-11-20

   function main
    p    = linspace(0,1,11);
    prob = linspace(0,1,100);
    x    = zeros(numel(p),numel(prob));
    for i = 1:numel(p)
      for j = 1:numel(prob)
        x(i,j) = INVCDF(p(i),prob(j));
      end
    end  
    plot(prob,x(1,:),prob,x(2,:),prob,x(3,:),prob,x(4,:),prob,x(5,:),...
         prob,x(6,:),prob,x(7,:),prob,x(8,:),prob,x(9,:),prob,x(10,:),...
         prob,x(11,:))
   end

   function x = INVCDF(p,prob)
     fun = @(x)CDF(p,x)-prob;
     x = fzero(fun,pi);  
   end

   function prob = CDF(p,x) 
     if x

 

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