How to compute log likelihood (which function to use) in Matlab the when the data is not normally distributed

savieklkdnf asked: 2022-06-29 machine learning, Statistics

Compute log-likelihood in MATLAB for non-normal data! Explore functions & methods beyond normal distributions. Get accurate results. Learn more now!

Expert Answer

John Williams answered . 2025-07-30 01:54:31

If you have the most recent release of the Statistics Toolbox:

>> x = poissrnd(4,20,1);
>> pd = fitdist(x,'poisson');
>> pd.NLogL
ans =
 39.0221

If you do not:

>> mu = poissfit(x);

>> -sum(log(poisspdf(x,mu)))

ans =

39.0221

To find maximum likelihood estimates (MLEs), you can use a negative loglikelihood function as an objective function of the optimization problem and solve it by using the MATLAB^® function fminsearch or functions in Optimization Toolbox™ and Global Optimization Toolbox. These functions allow you to choose a search algorithm and exercise low-level control over algorithm execution. By contrast, the mle function and the distribution fitting functions that end with fit, such as normfit and gamfit, use preset algorithms with options limited to those set by the statset function.

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