Additional information on finite mixture models for count data and a similar example are found in Deb, P., and P. K. Trivedi. 1997. Demand for medical care by the elderly: A finite mixture approach. Journal of Applied Econometrics 12: 313-336. https://doi.org/10.1002/(SICI)1099-1255(199705)12:3<313::AID-JAE440>3.0.CO;2-G.
Data are analyzed in Cameron, A. C., and P. K. Trivedi. 2010. Microeconometrics Using Stata. Rev. ed. College Station, TX: Stata Press.
Data on annual number of doctor visits for individuals age 65 and older       from the U.S. Medical Expenditure Panel Survey for 2003.