Question
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?
Expert Answer
John Williams
PhD Expert
Answered Aug 24, 2026
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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