🎯 点估计计算器（比例）Point Estimate Calculator (Proportion)
输入成功次数和试验次数，计算比例的四种点估计：最大似然（x/n）、拉普拉斯、Jeffreys 和 Wilson，并按常用规则给出推荐值。Enter the number of successes and trials to get four point estimates of a proportion — maximum likelihood (x/n), Laplace, Jeffreys and Wilson — with the one a common rule recommends.
使用说明与常见问题How-to & FAQ
「点估计计算器（比例）」是什么？What is the Point Estimate Calculator (Proportion) tool?
输入成功次数和试验次数，计算比例的四种点估计：最大似然（x/n）、拉普拉斯、Jeffreys 和 Wilson，并按常用规则给出推荐值。Enter the number of successes and trials to get four point estimates of a proportion — maximum likelihood (x/n), Laplace, Jeffreys and Wilson — with the one a common rule recommends.
如何使用「点估计计算器（比例）」？How do I use the Point Estimate Calculator (Proportion) tool?
在「点估计计算器（比例）」中，填写「成功次数 x」、「试验次数 n」、「置信水平（Wilson 用）」等参数，结果会随输入实时计算并显示在下方。In the Point Estimate Calculator (Proportion): Fill in "Successes x", "Trials n", "Confidence level (for Wilson)"; results are recalculated instantly as you type.
为什么不总是用 x/n？Why not always use x/n?
样本小或比例接近 0、1 时，x/n 会给出 0% 或 100% 这类极端值。拉普拉斯、Jeffreys 和 Wilson 估计会向 50% 适当收缩，通常更合理。With small samples or proportions near 0 or 1, x/n gives extreme values such as 0% or 100%. The Laplace, Jeffreys and Wilson estimates pull slightly toward 50% and are usually more sensible.
推荐规则从哪来？Where does the recommendation rule come from?
这是在线点估计计算器中常见的经验规则（x/n ≤ 0.5 用 Wilson、0.5 < x/n < 0.9 用最大似然、x/n ≥ 0.9 取 Jeffreys 与拉普拉斯中较小者），我们没有找到它的正式出处，分界点是任意的，也不是统计学标准，所以四个值都列出来供你选择。It is a rule of thumb common in online point-estimate calculators (Wilson if x/n ≤ 0.5, maximum likelihood if 0.5 < x/n < 0.9, the smaller of Jeffreys and Laplace if x/n ≥ 0.9). We found no formal source for it and the cut-offs are arbitrary, so all four estimates are shown.
置信水平影响什么？What does the confidence level change?
只影响 Wilson 估计（z 值越大越向 50% 收缩）。Only the Wilson estimate, which shrinks more toward 50% as z grows.
计算精度如何？How precise are the results?
「点估计计算器（比例）」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 Point Estimate Calculator (Proportion) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「点估计计算器（比例）」免费吗？需要注册吗？Is the Point Estimate Calculator (Proportion) free? Do I need an account?
「点估计计算器（比例）」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 Point Estimate Calculator (Proportion) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.