论文标题
分段概率分布理论
Piecewise Probability Distribution Theory
论文作者
论文摘要
考虑了带有空间符号及其层次特定情况的一般分段（包括刻有方向的）概率分布。获得了一般一维线性线性概率分布的显式闭合形式归一化，期望和方差以及中位和模式公式和算法。它们还适用于一般多边形或一维线性连续，概率分布，尤其是将其用于四方概率分布。最后一个分布和三角形概率分布作为进一步的情况的已知公式用于测试获得的公式和算法。
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the median and mode formulas and algorithms for a general one-dimensional piecewise linear probability distribution are obtained. They are also applied to a general polygonal, or one-dimensional piecewise linear continuous, probability distribution and, in particular, to a tetragonal probability distribution. The known formulas for the last distribution and a triangular probability distribution as a further particular case are used to test the obtained formulas and algorithms.
