Exact Modes and Antimodes of Two-Term Weighted Sums of Discrete Uniform Random Variables

This paper studies the weighted sum Z=aX+bY, where X and Y are independent discrete uniform random variables. The modes and antimodes of Z are determined by counting lattice points. When N=b, the antimodes are exactly the values with a unique representation. Their number is also obtained and eventually becomes 2ab.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-20
DOI
https://doi.org/10.5281/zenodo.22026238
Primary Topic
Random Matrices and Applications
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Exact Modes and Antimodes of Two-Term Weighted Sums of Discrete Uniform Random Variables

Po Hu
Zenodo (CERN European Organization for Nuclear Research)
Random Matrices and Applications
preprint

Exact Modes and Antimodes of Two-Term Weighted Sums of Discrete Uniform Random Variables

Po Hu
preprint en

Abstract

This paper studies the weighted sum Z=aX+bY, where X and Y are independent discrete uniform random variables. The modes and antimodes of Z are determined by counting lattice points. When N=b, the antimodes are exactly the values with a unique representation. Their number is also obtained and eventually becomes 2ab.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Random Matrices and Applications
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.