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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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