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[Explore Stack Internal](https://stackoverflow.co/internal/?utm_medium=referral&utm_source=stats-community&utm_campaign=side-bar&utm_content=explore-teams-compact-popover) # [Simulate from a zero-inflated poisson distribution](https://stats.stackexchange.com/questions/189005/simulate-from-a-zero-inflated-poisson-distribution) [Ask Question](https://stats.stackexchange.com/questions/ask) Asked 10 years, 1 month ago Modified [5 years, 8 months ago](https://stats.stackexchange.com/questions/189005/simulate-from-a-zero-inflated-poisson-distribution?lastactivity "2020-05-26 11:19:14Z") Viewed 9k times This question shows research effort; it is useful and clear 12 Save this question. Show activity on this post. I am trying to simulate from observed data that I have fit to a zero-inflated Poisson regression model. I fit the data in R using `zeroinfl()` from the package `pscl`, but I am having trouble figuring out how to derive the ZIP distribution from the coefficient estimates. I know how to derive the predicted counts from these coefficient estimates (more information here: <http://www.ats.ucla.edu/stat/stata/faq/predict_zip.htm>), but can anyone help me understand how to find/derive estimates for my distribution parameters (i.e. lambda for the Poisson distribution, p for the Bernoulli distribution) that I can then sample from? - [r](https://stats.stackexchange.com/questions/tagged/r "show questions tagged 'r'") - [simulation](https://stats.stackexchange.com/questions/tagged/simulation "show questions tagged 'simulation'") - [poisson-regression](https://stats.stackexchange.com/questions/tagged/poisson-regression "show questions tagged 'poisson-regression'") - [zero-inflation](https://stats.stackexchange.com/questions/tagged/zero-inflation "show questions tagged 'zero-inflation'") [Share](https://stats.stackexchange.com/q/189005 "Short permalink to this question") Share a link to this question Copy link [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/ "The current license for this post: CC BY-SA 4.0") Cite [Improve this question](https://stats.stackexchange.com/posts/189005/edit) Follow Follow this question to receive notifications [edited May 26, 2020 at 11:19](https://stats.stackexchange.com/posts/189005/revisions "show all edits to this post") [](https://stats.stackexchange.com/users/180771/kim) [Kim](https://stats.stackexchange.com/users/180771/kim) 17988 bronze badges asked Jan 2, 2016 at 22:00 [](https://stats.stackexchange.com/users/99561/lhz) [lhz](https://stats.stackexchange.com/users/99561/lhz) 12311 silver badge44 bronze badges [Add a comment](https://stats.stackexchange.com/questions/189005/simulate-from-a-zero-inflated-poisson-distribution "Use comments to ask for more information or suggest improvements. Avoid answering questions in comments.") \| ## 1 Answer 1 Sorted by: [Reset to default](https://stats.stackexchange.com/questions/189005/simulate-from-a-zero-inflated-poisson-distribution?answertab=scoredesc#tab-top) This answer is useful 25 Save this answer. Show activity on this post. You can get the probability of zero-inflation by ``` p <- predict(object, ..., type = "zero") ``` and the mean of the count distribution by ``` lambda <- predict(object, ..., type = "count") ``` See Appendix C of `vignette("countreg", package = "pscl")` for a few more details. To simulate the distribution, you can either do it manually with ``` ifelse(rbinom(n, size = 1, prob = p) > 0, 0, rpois(n, lambda = lambda)) ``` or you can use `rzipois()` from the `VGAM` package ``` library("VGAM") rzipois(n, lambda = lambda, pstr0 = p) ``` which essentially also does an `ifelse()` as above but adds a few sanity checks etc. [Share](https://stats.stackexchange.com/a/189052 "Short permalink to this answer") Share a link to this answer Copy link [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/ "The current license for this post: CC BY-SA 3.0") Cite [Improve this answer](https://stats.stackexchange.com/posts/189052/edit) Follow Follow this answer to receive notifications [edited Jan 3, 2016 at 16:44](https://stats.stackexchange.com/posts/189052/revisions "show all edits to this post") answered Jan 3, 2016 at 9:53 [](https://stats.stackexchange.com/users/60261/achim-zeileis) [Achim Zeileis](https://stats.stackexchange.com/users/60261/achim-zeileis) 16\.9k22 gold badges4343 silver badges6565 bronze badges 0 [Add a comment](https://stats.stackexchange.com/questions/189005/simulate-from-a-zero-inflated-poisson-distribution "Use comments to ask for more information or suggest improvements. Avoid comments like “+1” or “thanks”.") \| Start asking to get answers Find the answer to your question by asking. 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You can get the probability of zero-inflation by ``` p <- predict(object, ..., type = "zero") ``` and the mean of the count distribution by ``` lambda <- predict(object, ..., type = "count") ``` See Appendix C of `vignette("countreg", package = "pscl")` for a few more details. To simulate the distribution, you can either do it manually with ``` ifelse(rbinom(n, size = 1, prob = p) > 0, 0, rpois(n, lambda = lambda)) ``` or you can use `rzipois()` from the `VGAM` package ``` library("VGAM") rzipois(n, lambda = lambda, pstr0 = p) ``` which essentially also does an `ifelse()` as above but adds a few sanity checks etc.