have $$\symExpectation\!\left(
\frac{1}{2^
{-\symRegValVariate_1}\!+\ldots+2^{-\symRegValVariate_\symNumReg}}
\right)
\underset{\symNumReg\rightarrow \infty}{=}
\frac{1}{\symExpectation
(2^{-\symRegValVariate_1}+\ldots+2^{-\symRegValVariate_\symNumReg})}
=
\frac{1}{\symNumReg \symExpectation(2^{-\symRegValVariate})}.$$ Together with we obtain $$\symPoissonRate
=
\symExpectation\left(
\frac{\symAlpha_\infty\,\symNumReg^2\,\symPowerSeriesFunc(\log_2( \symPoissonRate/\symNumReg))}{2^{-\symRegValVariate_1}+\ldots+2^{-\symRegValVariate_\symNumReg}}
\right)
\quad
\text{for $\symNumReg\rightarrow \infty$}.$$ Therefore, the asymptotic relative bias of $$\symPoissonRateEstimate 
= 
\frac{\symAlpha_\infty\,\symNumReg^2}{2^{-\symRegValVariate_1}+\ldots+2^{-\symRegValVariate_\symNumReg}}$$ is bounded by $\symEpsPowerSeriesFunc$, which makes this statistic a good estimator for the Poisson parameter. It also corresponds to the raw estimator , if the Poisson parameter estimate is used as cardinality estimate as discussed in \[sec:poisson\_approximation\].

Limitations of the Raw Estimator
--------------------------------

The raw estimator is based on two prerequisites. In practice, only the first requiring $\symNumReg$ to be sufficiently large is satisfied. However, the second assuming that the distribution of register values can be approximated by is not always true. A random variable $\symRegValVariate'$ with cumulative distribution function can be transformed into a random variable $\symRegValVariate$ with cumulative distribution function using $$\label{equ:dist_transformation}
\symRegValVariate = \min\!\left(\max\!\left(\symRegValVariate',0\right), \symRegRange+1\right).$$ Therefore, register values $\symRegValVariate_1,\ldots,\symRegValVariate_\symNumReg$ can be seen as the result after applying this transformation to a sample $\symRegValVariate'_1,\ldots,\symRegValVariate'_\symNumReg$ from . If all registers values are in the range $[1,\symRegRange]$, they must be identical to the values $\symRegValVariate'_1,\ldots,\symRegValVariate'_\symNumReg$. In other words, the observed register values are also a plausible sample of distribution . Hence, as long as all 