Initial condition for maximum likelihood estimation (MLE)

When using the maximum likelihood estimation (MLE) command in MATLAB (https://www.mathworks.com/help/stats/mle.html#btt7ilj) for a Weibull 2 parameter distribution, how do you specificy the initial conditions? Also, if you just type in the Weibull distribution for the MLE command, why is it that MATLAB can find the values directly without entering the initial conditions? Thanks!

Answer 1

[Shantanu Dixit]

Hi Susan,

When using the 'mle' function in MATLAB, defining initial conditions is not necessary when working with built-in distributions such as 'Weibull'. MATLAB can estimate the parameters without requiring initial conditions in these cases.

However, initial conditions become necessary when working with custom distributions defined using 'pdf', 'logpdf', or 'nloglf'. In such cases, you can specify initial parameter values using the 'Start' name-value pair.

data = wblrnd(2, 3, 300, 1); 
phat = mle(data, 'Distribution', 'Weibull');
disp('Estimated Parameters (Scale, Shape):');

Estimated Parameters (Scale, Shape):

disp(phat)

    1.9693    3.0718

Additionally you can refer to the following useful MathWorks documentation:

• mle: https://www.mathworks.com/help/stats/mle.html
• wblrnd: https://www.mathworks.com/help/stats/wblrnd.html

Hope this helps!