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2021年11月14日 (日) 18:00的版本

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→‎Confidence interval 置信区间Confidence interval

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=== ~~Confidence interval '''置信区间Confidence interval '''~~===

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=== 置信区间===

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The [[confidence interval]] for the mean of a Poisson distribution can be expressed using the relationship between the cumulative distribution functions of the Poisson and [[chi-squared distribution]]s. The chi-squared distribution is itself closely related to the [[gamma distribution]], and this leads to an alternative expression. Given an observation ''k'' from a Poisson distribution with mean ''μ'', a confidence interval for ''μ'' with confidence level {{math|1 – α}} is

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The confidence interval for the mean of a Poisson distribution can be expressed using the relationship between the cumulative distribution functions of the Poisson and chi-squared distributions. The chi-squared distribution is itself closely related to the gamma distribution, and this leads to an alternative expression. Given an observation k from a Poisson distribution with mean μ, a confidence interval for μ with confidence level is

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置信区间的平均泊松分布可以用泊松分布和卡方分布的累积分布函数之间的关系来表示。卡方分布本身与伽玛分布密切相关，这导致了另一种表达方式。给定一个来自平均泊松分布的观测值''k''，一个带有置信水平{{math|1 – α}}和置信区间''μ''是

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:<math>k=\sum_{i=1}^n k_i ,\!</math>

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