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I have a non-count data with huge number of zeros in the target variable. I need to fit a model being a mixture of Dirac delta function and normal distribution parametrized by mean $X\beta$ and variance $\sigma^2$, with mixing proportion $\pi$, i.e.

$$ y \sim \left\{ \begin{array}{cl} 0 & \text{ with probability }\pi \\ \mathcal{N}\left(X \beta, \sigma^2 \right) & \text{ with probability } 1-\pi\end{array} \right.$$

to account for the excess zeros. Could you provide me with any references about such models? Or maybe there is some approach that is better, then the above, for continuous, zero-inflated data?

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    $\begingroup$ If you have a genuine expectation that the true distribution is indeed a zero-inflated normal, then just fit that model and be done with it. Whether other approaches are better depends on whether the expectation/evidence that some other choice of distribution is a better approximation to nature. Edited to add: it seems an odd sampling process that both deals with continuous data and has a huge number of integers (zeros) in it. $\endgroup$ Jun 1, 2017 at 14:35
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    $\begingroup$ @user43849 the process that produces such data is very easy to imagine: think of some kind of device that is idle for most of the time, but sometimes fires some continuous signals. $\endgroup$
    – Tim
    Jun 1, 2017 at 14:43
  • $\begingroup$ Interestingly, the Wiki excerpt of the zero-inflation tag says there is zero-inflated normal regression. Not that this would help, but I find it curious. $\endgroup$ Jun 1, 2017 at 14:46
  • $\begingroup$ @RichardHardy I wasn't able to find any references dealing with such models, this is how the question emerged... $\endgroup$
    – Tim
    Jun 1, 2017 at 14:51
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    $\begingroup$ In Epidemiology, this is a common problem and the term for such variables is "spike at zero". However, all methods that I am aware of are assuming non-negative values. But maybe the term helps to find extensions to negative values. $\endgroup$
    – LuckyPal
    May 25, 2021 at 16:10

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I have found 2 references so far using zero-inflated normal regression, one in medical research and the other in animal conservation:

Both the response variables, Agatston scores of CAC and the number of fledglings of brood, are probably non-negative, however.

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