🎯 泊松分布计算器Poisson Distribution Calculator
输入平均发生次数 λ 和次数 k，计算泊松分布的 P(X = k)、P(X ≤ k)、P(X < k)、P(X ≥ k) 和 P(X > k)，并给出均值、方差和标准差。Enter the average rate λ and a count k to get the Poisson probabilities P(X = k), P(X ≤ k), P(X < k), P(X ≥ k) and P(X > k), with the mean, variance and standard deviation.
使用说明与常见问题How-to & FAQ
「泊松分布计算器」是什么？What is the Poisson Distribution Calculator tool?
输入平均发生次数 λ 和次数 k，计算泊松分布的 P(X = k)、P(X ≤ k)、P(X < k)、P(X ≥ k) 和 P(X > k)，并给出均值、方差和标准差。Enter the average rate λ and a count k to get the Poisson probabilities P(X = k), P(X ≤ k), P(X < k), P(X ≥ k) and P(X > k), with the mean, variance and standard deviation.
如何使用「泊松分布计算器」？How do I use the Poisson Distribution Calculator tool?
在「泊松分布计算器」中，填写「平均次数 λ」、「次数 k（非负整数）」等参数，结果会随输入实时计算并显示在下方。In the Poisson Distribution Calculator: Fill in "Average rate λ", "Count k (whole number, 0 or more)"; results are recalculated instantly as you type.
泊松分布公式？What is the Poisson formula?
P(X = k) = λ^k · e^(−λ) ÷ k!。工具用对数逐项累加计算，λ 很大时也不会溢出。P(X = k) = λ^k · e^(−λ) ÷ k!. The tool accumulates terms in log space so large λ does not overflow.
什么情况适用泊松分布？When does the Poisson model apply?
事件在固定时间或空间内独立发生、平均发生率恒定，例如每小时来电数、每页错字数。λ 是这个区间内的平均次数。When events happen independently at a constant average rate in a fixed interval of time or space, such as calls per hour or typos per page. λ is the average count in that interval.
结果精确到多少？How precise are the results?
概率显示到小数点后 10 位，小于 0.0001 的值用科学记数法显示（6 位有效数字）。很小的右尾概率 P(X > k)、P(X ≥ k) 直接逐项求和，而不是用 1 减去累积概率，避免相减带来的精度损失；小于约 10⁻³⁰⁸ 的概率超出双精度范围，按对数换算后显示（如 5.5×10⁻⁶⁸⁰）。Probabilities are shown to 10 decimal places, and values below 0.0001 in scientific notation (6 significant digits). Small right-tail probabilities P(X > k) and P(X ≥ k) are summed term by term instead of 1 minus the cumulative probability, which avoids cancellation error; probabilities below about 10⁻³⁰⁸ are outside double precision and are shown via logarithms (such as 5.5×10⁻⁶⁸⁰).
「泊松分布计算器」免费吗？需要注册吗？Is the Poisson Distribution Calculator free? Do I need an account?
「泊松分布计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Poisson Distribution Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.