[R] Obtaining a value of pie in a zero inflated model (fm-zinb2)

[Sorkin, John]

I am running a zero inflated regression using the zeroinfl function similar to the model below:
  
 fm_zinb2 <- zeroinfl(art ~ . | ., data = bioChemists, dist = "poisson")
summary(fm_zinb2)

I have three questions:

1) How can I obtain a value for the parameter pie, which is the fraction of the population that is in the zero inflated model vs the fraction in the count model? 

2) For any particular subject, how can I determine if the subject is in the portion of the population that contributes a zero count because the subject is in the group of subjects who have structural zero responses vs. the subject being in the portion of the population who can contribute a zero or a non-zero response?

3) zero inflated models can be solved using closed form solutions, or using iterative methods. Which method is used by fm_zinb2?

Thank you,
John

John David Sorkin M.D., Ph.D.
Professor of Medicine, University of Maryland School of Medicine;

Associate Director for Biostatistics and Informatics, Baltimore VA Medical Center Geriatrics Research, Education, and Clinical Center; 

PI Biostatistics and Informatics Core, University of Maryland School of Medicine Claude D. Pepper Older Americans Independence Center;

Senior Statistician University of Maryland Center for Vascular Research;

Division of Gerontology and Paliative Care,
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
Cell phone 443-418-5382