Re: Fitting Zero Inflated ModelsHi @Aziza,
There are already some zero-inflated modeling possibilities in the platform "Fit Model" :
When you choose "Generalized Regression", at the end of the options for the Distribution, you can find some zero-inflated distributions type : binomial, beta binomial, Poisson, Gamma, ...
You can find more infos about the available distributions in this platform here : Specify a Distribution (jmp.com)
Maybe the distributions proposed won't be of any help to you, but just wanted to inform you in case it could help you 
Best,
Re: Fitting Zero Inflated Models@Aziza also, to clarify, the ZI models that @Victor_G describes in Generalized Regression and are available in JMP Pro.
Fitting Zero Inflated Models
What inspired this wish list request? JMP does not seem to have a built-in support for zero-inflated models?
What is the improvement you would like to see? Possibility to fit zero-inflated model in JMP
Why is this idea important? It occurs quite often that the response is zero-inflated. Zero-inflated models are used when the response variable has a large number of zero values and a continuous, non-negative distribution for the non-zero values. Zero-inflated models combine two separate models: one for predicting the probability of a zero outcome, and another for predicting the non-zero values.
Advanced Statistical ModelingBasic Data Analysis and ModelingData Exploration and VisualizationDesign of Experiments
