Imputation of variable from a mixture distribution - multiple imputation using mice in R

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I have a dataset with missing data that I need to impute, I am using the mice package in R to do so.

One of my variables has a mixture distribution, where X = 0, or X ~ N(mu,std). So X is either equal to zero, or it is drawn from some normal distribution. I can tell this from looking at the distribution of values which are not missing.

Therefore, when imputing I would like to first impute whether X=0 or not. If not, then I will impute its value from the normal distribution using predictive mean matching (as is standard in mice). However I am unsure how to code this.

I have been using this text: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3074241/ to teach myself how to implement the package properly, but cannot find anything about variables distributed like this (i.e. from a mixture of two distributions).

Alternatively, would just using predictive mean matching impute this variable correctly, giving the mixture distribution?

imputationr-micemixture

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