For the zero-truncated Poisson distribution, is the unique integrable nonrandomized unbiased estimator of . Indeed unbiasedness gives , and power series coefficients force the parity values. Its variance is ; clipping it to gives mean squared error , strictly smaller for .
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The Zero-Truncated Poisson (ZTP) distribution is a probability distribution that is derived from the Poisson distribution by removing the zero-count outcomes. This modification is useful in scenarios where the occurrence of an event is guaranteed to be at least one, hence no observations of zero are possible.