Calculate Negative loglikelihood of custom probability distribution

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dj1du 2022-8-20

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https://ww2.mathworks.cn/matlabcentral/answers/1782405-calculate-negative-loglikelihood-of-custom-probability-distribution

评论： Torsten 2022-8-21

Hello,

I have a 1D vector, whose data are chi distributed. The Matlab built-in function negloglik expects a probability distribution object pd, which for standard distributions can be created by fitdist. Unfortunately, my chi distribution is no standard distribution and is thus not supported by fitdist.

How can I calculated the Negative loglikelihood in my special case?

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Torsten 2022-8-20

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https://ww2.mathworks.cn/matlabcentral/answers/1782405-calculate-negative-loglikelihood-of-custom-probability-distribution#answer_1029720

编辑：Torsten 2022-8-20

在 MATLAB Online 中打开

% Generate random numbers from chi distribution with k = 6

k = 6;

y = rand(150,1);

x = gammaincinv(y,k/2);

x = sqrt(2*x);

% Recover k by maximum likelihood estimate

syms k

f = prod(x.^(k-1).*exp(-x.^2/2)/(2^(k/2-1)*gamma(k/2)));

logf = log(f)

logf =

dlogfdk = simplify(diff(logf,k))

dlogfdk =

knum = vpasolve(dlogfdk==0,k,[0 10])

knum =

6.2804404606724144851804043896857

negative_log_likelihood = subs(-logf,k,knum)

negative_log_likelihood =

148.38329537359329151154663411951

k = 0:0.1:10;

Logf = matlabFunction(logf);

plot(k,-Logf(k))

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dj1du 2022-8-20

One concluding question: Beside the negative loglikelihood, is it possible to calculate the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) in a similar manner? These two latter criteria are said to provide a better determination of the 'best' fitting distribution.