Let's say we have a population distributed by Zero-inflated Poisson distribution:

$$ f(x | \psi, \lambda) = \left\{ \begin{array}{ll} 1-\psi + \psi e^{-\lambda} & \mbox{if } x = 0 \\ \psi \frac {\lambda^x e^{-\lambda x}}{x!} & \mbox{if } x > 0 \end{array} \right. $$

and then a sample with size $N_s$ and known parameters $\psi_s$ and $\lambda_s$.

How can I estimate the confidence intervals for the parameters $\psi$ and $\lambda$?


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