We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is equivalent to running a rectangular low-pass filter over the spacing, which simplifies the expressions for the expected values and introduces correlations between overlapping intervals.

翻译：我们将区间间距定义为数据在特定宽度间隔上的顺序统计量之差。针对均匀分布、指数分布和逻辑分布变量，我们推导了其概率密度函数、期望值与方差。研究表明，区间间距等效于在间距上运行矩形低通滤波器，这不仅简化了期望值的表达式，还引入了重叠区间之间的相关性。