CODEWITHSUNDEEP
matlaboptimizationparametersdistributioncurve-fitting
Nicknock82
Nicknock82

Reputation: 1

Fitting a distribution with Matlab?

I have data on Italian city size from 2011 census and I would like to fit them with a Double Pareto LogNormal but I cannot. I tried defining a function handle that is the log likelihood of the distribution in this way

ln_lik_dpln=@(alpha,beta,mu,sigma)                                         ...
    - sum(log(alpha) + log(beta) - log(alpha+beta) +                       ...
    normpdf((pop2011-mu)/sigma) +                                          ...
    log(normpdf((alpha*sigma)-((pop2011-mu)/sigma))/normcdf((alpha*sigma)- ...
    ((pop2011-mu)/sigma)) +                                                ...
    normpdf((beta*sigma)-((pop2011-mu)/sigma))/normcdf((beta*sigma) -      ...
    ((pop2011-mu)/sigma))))

and then minimizing it with fmincon and fminunc but both do not recognize beta.

Upvotes: 0

Views: 193

Answers (1)

transversality condition
transversality condition

Reputation: 791

You need to write your anonymous function so that its parameters are described by a single vector rather than multiple scalar arguments. E.g., 

ln_lik_dpln=@(x) ...
    - sum(log(x(1)) + log(x(2)) - log(x(1)+x(2)) + ...
    normpdf((pop2011-x(3))/x(4)) + ...
    log(normpdf((x(1)*x(4))-((pop2011-x(3))/x(4)))/normcdf((x(1)*x(4))- ...
    ((pop2011-x(3))/x(4))) + ...
    normpdf((x(2)*x(4))-((pop2011-x(3))/x(4)))/normcdf((x(2)*x(4)) ...
    ((pop2011-x(3))/x(4)))))​

Then you can pass this function handle to fmincon or fminunc for minimization from some initial vector of length 4.

Upvotes: 1

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