参数估计¶

矩估计法¶

1. 求数学期望：\(u_1 = E(X) = f(\theta)\)

2. 求反函数：\(\theta = f^{-1}(u_1)\)

3. 将样本值代入反函数，得到参数的估计值：\(\hat{\theta} = f^{-1}(\bar{X})\)

最大似然估计法¶

1. 构造似然函数：\(L(\theta) = \prod_{i=1}^n f(x_i; \theta)\)

2. 取对数：\(\ln L(\theta) = \sum_{i=1}^n \ln f(x_i; \theta)\)

3. 求导数：\(\frac{d}{d\theta} \ln L(\theta) = 0\)

4. 解方程：\(\hat{\theta} = f^{-1}(\bar{X})\)

无偏估计¶