Article

A catch-all discrete distribution: Short description and main properties

Examples and Counterexamples

Fachada, Nuno; Matos-Carvalho, João P.; Fernandes, Carlos M. — 2025 — Elsevier

Key information

Authors:

Fachada, Nuno (Nuno Fachada); Matos-Carvalho, João P.; Fernandes, Carlos M. (Carlos Miguel da Costa Fernandes)

Published in

22/08/2025

Abstract

Consider a population of size N where each element has an independent probability p of being a success. By sampling this population without replacement, how many elements need to be drawn to find all successes? This paper describes this discrete distribution, derives its main properties, and validates the results through simulation.

Publication details

Authors in the community:

Publication version

VoR - Version of Record

Publisher

Elsevier

Link to the publisher's version

https://www.sciencedirect.com/science/article/pii/S2666657X25000230

Title of the publication container

Examples and Counterexamples

First page or article number

100196

Volume

8

ISSN

2666-657X

Fields of Science and Technology (FOS)

mathematics - Mathematics

Keywords

  • Discrete distribution
  • All successes
  • Empirical validation
  • Simulation analysis

Publication language (ISO code)

eng - English

Rights type:

Open access

Creative Commons license

CC-BY - CC-BY

Financing entity

Fundação para a Ciência e a Tecnologia

Identifier for the funding entity: https://doi.org/10.13039/501100001871

Type of identifier of the funding entity: Crossref Funder

Number for the project, award or grant: UIDB/04111/2020

Financing entity

Fundação para a Ciência e a Tecnologia

Identifier for the funding entity: https://doi.org/10.13039/501100001871

Type of identifier of the funding entity: Crossref Funder

Number for the project, award or grant: UIDB/00066/2020

Financing entity

Fundação para a Ciência e a Tecnologia

Identifier for the funding entity: https://doi.org/10.13039/501100001871

Type of identifier of the funding entity: Crossref Funder

Number for the project, award or grant: UIDB/00408/2025

Financing entity

Fundação para a Ciência e a Tecnologia

Identifier for the funding entity: https://doi.org/10.13039/501100001871

Type of identifier of the funding entity: Crossref Funder

Number for the project, award or grant: CEECINST/00002/2021/CP2788/CT0001

Financing entity

Universidade Lusófona de Humanidades e Tecnologias

Identifier for the funding entity: https://doi.org/10.13039/501100021538

Type of identifier of the funding entity: Crossref Funder

Number for the project, award or grant: COFAC/ILIND/COPELABS/1/2024

Financing entity

Ministerio de Ciencia, Innovación y Universidades

Funding Stream: MICIU/AEI/10.13039/501100011033

Identifier for the funding entity: https://doi.org/10.13039/100014440

Type of identifier of the funding entity: Crossref Funder

Number for the project, award or grant: PID2023-147409NB-C21