Marginal likelihood function of a fragile survival model and the Laplace transform

[TomHsiung]

Hello, guys

AI and textbooks give me two different version of marginal likelihood functions in the estimation for parameters of a fragile survival model. I don't which one is correct. However, I prefer the answer given by Gemini since it is more logical as well as that it uses the Laplace transform. What do you think? Thanks.

Please compare them in the screenshots below.

A, the marginal likelihood function given by a textbook

B, the marginal likelihood function given by Gemini

[JacobSimonsen · Accepted solution]

Hi Tom,

I prefer the textbook. It is most logical for me.

and btw, it is not gemini that came up with the solution gemini shows. Gemini has it from somewhere. You would also not say cite google for a result, even that you found it using google.

Best, Jacob

[TomHsiung]

Hi, Jacob

Thank you for your feedback and I agree with you. The likelihood function on the textbook is a good way for parameter estimation. I looked up in the SAS document and found SAS can provide two distributions for U, including gamma distribution and the other which I forget the name. Much appreciated!