Normal approximation to negative binomial distribution-1

Normal approximation to the Negative Binomial is valid when the number of required successes, $s$, is large, and the probability of success, $p$, is neither very small nor very large. This approximation can be justified via Central Limit Theorem, because the NegBin($s$, $p$) distribution can be thought of as the sum of $s$ independent NegBin(1, $p$) distributions. In practice, some difficulty is knowing whether the values for $s$ and $p$ fall within the bounds for which the Normal distribution is a good approximation. The smaller the value of $p$, the longer the tail of a NegBin(1,$p$) distribution would be.
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http://www.vosesoftware.com/ModelRiskHelp/index.htm#Distributions/Approximating_one_distribution_with_another/Approximations_to_the_Negative_Binomial_distribution.htm
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Vose Software
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Ivo Dinov
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Vose Software
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