Small Sample Distributions for Multi-Sample Statistics of the Smirnov Type
Small Sample Distributions for Multi-Sample Statistics of the Smirnov Type
Let \begin{equation*}\tag{1.1}X^{(i)}_1,X^{(i)}_2, \cdots, X^{(i)}_{n_i},\qquad i = 1, 2, \cdots, c,\end{equation*} be samples of $c$ independent random variables $X^{(i)}$ with continuous cumulative distribution functions $F^{(i)}$, and let \begin{equation*}\begin{align*}F^{\ast^{(i)}}(x) &= 0\qquad x &< X^{(i)}_1 \\ \tag{1.2}F^{\ast^{(i)}} (x) &= k/n_i\qquad X^{(1)}_k &\leqq x < X^{(1)}_{k+1}, 1 \leqq k < n_i \\ F^{\ast^{(i)}} (x) …