How does JMP optimize the competing risk mixture in the life distribution platform (what method is used)? Thank you!
Do you mean inference method? It is maximum likelihood.
No. The optimization method for finding MLE is Newton-Raphson in Life Distribution. E-M could be an alternative for finding MLE in this case, but it is not the only approach.
The likelihood function of a competing risk mixture has the same general form regardless what distribution is involved. The definition of the likelihood in this context can be found in Section 2.4 Likelihood in Statistical Methods for Reliability Data, by Meeker and Escobar.
The likelihood function of a competing risk mixture, in particular, is obtained by replacing the corresponding functions in that section by corresponding functions of the competing risk distribution, whose definition can be found in section 15.2.2 Systems with Components in Series, from the same book. The section defines the distribution function, but survival function and density function can be derived accordingly.
