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arXiv · 2201.12730

Piecewise Probability Distribution Theory

Lev Gelimson
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Abstract

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.

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Lev Gelimson. 2022-01-30. Piecewise Probability Distribution Theory. https://arxiv.org/abs/2201.12730

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