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<p>This paper describes an interesting class of discrete probability distributions that arise from the discretization of continuous distributions. They are sometimes also called telescopic distributions, a term inspired by the concept of “telescoping series" in mathematics. After some introductory remarks, we will focus primarily on deriving two-dimensional telescopic distributions, i.e., discretized two-dimensional continuous probability distributions, which are typically constructed using a suitable copula. We will then present examples using both simulated and real data to demonstrate the advantages and potential applications of these models. Among other things, we will derive and apply the “telescopic" form of the bivariate negative binomial distribution.</p>

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On bivariate telescopic distributions of probability and their application

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Petr Volf

摘要

This paper describes an interesting class of discrete probability distributions that arise from the discretization of continuous distributions. They are sometimes also called telescopic distributions, a term inspired by the concept of “telescoping series" in mathematics. After some introductory remarks, we will focus primarily on deriving two-dimensional telescopic distributions, i.e., discretized two-dimensional continuous probability distributions, which are typically constructed using a suitable copula. We will then present examples using both simulated and real data to demonstrate the advantages and potential applications of these models. Among other things, we will derive and apply the “telescopic" form of the bivariate negative binomial distribution.