The H probability distributions
DOI:
https://doi.org/10.17721/1812-5409.2026/1.11Keywords:
extended β−Benford distribution, Bernstein polynomials, number system, universal properties of a probability distribution, homotopic simplicial complexAbstract
Probability distributions are important models in all scientific fields; however, they are essential in statistics. We provide a new class of mixed joint probability distributions with probability spaces that are sequences of nested piled 2D−lattices. The methodology for producing these models involves embedding a discrete variable extended β−Benford’s distribution into a continuous variable modified Bernstein polynomial. β is the parameter of this family of distributions and denotes the base of an arbitrary number system. Our purpose was to describe the mathematical structure and statistical features behind the interactions of these probability distributions. On the basis of the theoretical development and its results, we conclude that these models are valuable for numerous applications in various scientific disciplines. A concrete decimal system case is introduced to support our hypothesis.
Pages of the article in the issue: 87 - 100
Language of the article: English
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