In the MATLAB stats tutorials there is a section called "Fitting a More Complicated Distribution: A Mixture of Two Normals" http://www.mathworks.com/help/stats/examples/fitting-custom-univariate-distributions.html
pdf_normmixture = @(x,p,mu1,mu2,sigma1,sigma2) ...
p*normpdf(x,mu1,sigma1) + (1-p)*normpdf(x,mu2,sigma2);
lb = [0 -Inf -Inf 0 0];
ub = [1 Inf Inf Inf Inf];
start = [pStart muStart sigmaStart sigmaStart];
paramEsts = mle(x, 'pdf',pdf_normmixture, 'start',start, 'lower',lb, 'upper',ub)
It uses MLE to estimate numerically the values
" [...] = MLE(DATA,'pdf',PDF,'cdf',CDF,'start',START,...) returns MLEs for the parameters of the distribution defined by the probability density and cumulative distribution functions PDF and CDF. PDF and CDF are function handles created using @. They accept as inputs a vector of data and one or more individual distribution parameters, and return vectors of probability density values and cumulative probability values, respectively. If the 'censoring' name/value pair is not present, you may omit the 'cdf' name/value pair. MLE computes the estimates by numerically maximizing the distribution's log-likelihood, and START is a vector containing initial values for the parameters."
I would like to apply the same methodology for fitting two or more normals to a univariate set of values that I have, but within a periodic domain. That is, angles that have values of 0° to 360° linked together as a circular range. I am not sure how to declare it in order to make MATLAB understand this kind of terminology.
Would it be possible to change this implementation to add the circular range case?
