 Count-mixture structural zero

A structural-zero component in a count mixture produces a count identically equal to zero. If its mixture weight is $\pi$ and the ordinary component also assigns mass $p_0$ to zero, the observed zero probability is $\pi +(1-\pi )p_0$. Thus an observed zero does not reveal the latent component membership. A shared component for a repeated count profile makes the whole profile zero and induces dependence between its components.