Statistics 简明教程

Statistics - Best Point Estimation

点估计涉及使用样本数据来计算一个单值（称为统计量），该值用作未知（固定或随机）总体参数的“最佳猜测”或“最佳估计”。更正式地说，它将点估计器应用于数据。

Point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" or "best estimate" of an unknown (fixed or random) population parameter. More formally, it is the application of a point estimator to the data.

Formula

其中——

Where −

  1. ${MLE}$ = Maximum Likelihood Estimation.

  2. ${S}$ = Number of Success .

  3. ${T}$ = Number of trials.

  4. ${z}$ = Z-Critical Value.

Example

Problem Statement −

Problem Statement −

如果在 99% 置信区间水平上，在 9 次试验中掷硬币 4 次，那么该硬币的最佳成功点是多少？

If a coin is tossed 4 times out of nine trials in 99% confidence interval level, then what is the best point of success of that coin?

Solution −

Solution −

成功 (S) = 4 试验 (T) = 9 置信区间水平 (P) = 99% = 0.99。为了计算最佳点估计，让我们计算所有值 −

Success(S) = 4 Trials (T) = 9 Confidence Interval Level (P) = 99% = 0.99. In order to compute best point estimation, let compute all the values −

Step 1 -

Step 1 −

Step 2 -

Step 2 −

Step 3 -

Step 3 −

Step 4 -

Step 4 −

从 Z 表中求出 Z 临界值。Z 临界值 (z) = 对于 99% 水平 = 2.5758

Discover Z-Critical Value from Z table. Z-Critical Value (z) = for 99% level = 2.5758

Step 5 -

Step 5 −

Result

因此，最佳点估计为 0.468，因为 MLE ≤ 0.5

Accordingly the Best Point Estimation is 0.468 as MLE ≤ 0.5

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