📊 负二项分布Negative Binomial Distribution Calculator
每次成功概率为 p，第 r 次成功恰好出现在第 k 次试验的概率 P(X = k) = C(k-1, r-1) pʳ (1-p)ᵏ⁻ʳ，以及累计概率、均值和方差。本地处理。With success probability p, the chance that the r-th success happens exactly on trial k is P(X = k) = C(k-1, r-1) pʳ (1-p)ᵏ⁻ʳ; plus cumulative probabilities, mean and variance. Processed locally.
使用说明与常见问题How-to & FAQ
「负二项分布」是什么？What is the Negative Binomial Distribution Calculator tool?
每次成功概率为 p，第 r 次成功恰好出现在第 k 次试验的概率 P(X = k) = C(k-1, r-1) pʳ (1-p)ᵏ⁻ʳ，以及累计概率、均值和方差。本地处理。With success probability p, the chance that the r-th success happens exactly on trial k is P(X = k) = C(k-1, r-1) pʳ (1-p)ᵏ⁻ʳ; plus cumulative probabilities, mean and variance. Processed locally.
如何使用「负二项分布」？How do I use the Negative Binomial Distribution Calculator tool?
填写成功次数 r、成功概率 p 和试验次数 k，即可得到第 r 次成功恰好发生在第 k 次试验的概率，以及累积概率、均值和方差。结果会随输入实时更新。Enter the successes r, the success probability p and the trial number k to get the probability that the r-th success happens exactly on trial k, plus cumulative probabilities, the mean and the variance. The result updates as you type.
另一种定义？Other definition?
有的教材用"第 r 次成功前的失败次数" Y = X - r；两者只差一个平移。Some texts count failures before the r-th success, Y = X - r - just a shift.
能举个计算实例吗？Can you show a worked example?
例如在「负二项分布」中填 成功次数 r = 3，成功概率 p = 0.5，试验次数 k = 10，结果区显示：P(X = k)：0.03515625；P(X ≤ k)：0.9453125；P(X > k)：0.0546875；均值 r/p：6；方差：6For example, entering Successes r = 3, Success probability p = 0.5, Trial number k = 10 in the Negative Binomial Distribution Calculator gives: P(X = k): 0.03515625; P(X ≤ k): 0.9453125; P(X > k): 0.0546875; Mean r/p: 6; Variance: 6
哪些输入会被检查？Which inputs are validated?
「负二项分布」会检查这些输入——「成功次数 r」：必须填写，不能为负数，须为整数；「成功概率 p」、「试验次数 k」：必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Negative Binomial Distribution Calculator checks its inputs — "Successes r": required, cannot be negative, must be a whole number; "Success probability p", "Trial number k": required; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「负二项分布」的设置：「成功次数 r」默认 3；「成功概率 p」默认 0.5；「试验次数 k」默认 10。每次生成结果都按当前设置处理。Settings in the Negative Binomial Distribution Calculator — "Successes r" default 3; "Success probability p" default 0.5; "Trial number k" default 10. The result always uses the current settings.
计算精度如何？How precise are the results?
「负二项分布」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Negative Binomial Distribution Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「负二项分布」免费吗？需要注册吗？Is the Negative Binomial Distribution Calculator free? Do I need an account?
「负二项分布」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 Negative Binomial 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.