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多元正态总体均值的序贯估计AI 解读

This article is a multivariate generalization of the sequential sampling procedure developed by Robbins (1959) and extended by Starr (1966b) for estimating the mean of a normal population when the scale parameter is unknown. The exact distribution of the stopping time is derived for the sequential procedure, and a recursive method for computing the distribution of the stopping time is proposed that can be easily programmed for mechanical calculation. It is shown that the…

通过线性回归刻画指数分布及相关分布AI 解读

Let $X_1, \cdots, X_n (n \geqslant 2)$ be a random sample on a rv $X$, and $Y_1 < \cdots < Y_n$ be the corresponding order statistics. Define $Z_k = \frac{1}{n-k}\Sigma^n_{i=k+1}(Y_i - Y_k), 1 \leqslant k \leqslant n - 1, W_k = \frac{1}{k-1}\Sigma^{k-1}_{i=1}(Y_k - Y_i),$ $2 \leqslant k \leqslant n$. Using the properties $E(Z_k\mid Y_k = y) = \alpha y + \beta$ and $E(W_k\mid Y_k = y) = \alpha y + \beta$, a.e. $(dF)$, where $\alpha$ and $\beta$ are constants, we obtain…