Population growth and geometrically thinned extreme value theory

M. Fátima Brilhante; M. Ivette Gomes; Sandra Mendonça; Dinis Pestana; Pedro Pestana

doi:10.1007/978-3-031-68949-9_2

Population growth and geometrically thinned extreme value theory

M. Fátima Brilhante
, M. Ivette Gomes
, Sandra Mendonça
, Dinis Pestana^*
, Pedro Pestana

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Starting from the simple Beta(2,2) model, connected to the Verhulst logistic parabola, several extensions are discussed, and connections to extremal models are revealed. Aside from the classical general extreme value model, extreme value models in randomly stopped extremes schemes are also discussed. Logistic and Gompertz growth equations are the usual choice to model sustainable growth. Therefore, observing that the logistic distribution is (geo)max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, other growth models, related to classical and to geometrically thinned extreme value theory are investigated.

Original language	English
Title of host publication	New frontiers in statistics and data science
Subtitle of host publication	SPE2023
Editors	Lígia Henriques-Rodrigues, Raquel Menezes, Luís Meira Machado, Susana Faria, Miguel de Carvalho
Publisher	Springer
Pages	13-26
Number of pages	14
ISBN (Electronic)	9783031689499
ISBN (Print)	9783031689482, 9783031726071
DOIs	https://doi.org/10.1007/978-3-031-68949-9_2
Publication status	Published - Jan 2025
Event	26th Congress of the Portuguese Statistical Society, SPE 2023 - Evora, Portugal Duration: 13 Oct 2021 → 16 Oct 2021

Publication series

Name	Springer Proceedings in Mathematics and Statistics
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	26th Congress of the Portuguese Statistical Society, SPE 2023
Country/Territory	Portugal
City	Evora
Period	13/10/21 → 16/10/21

Keywords

BetaBoop random variables
Extreme value theory
Generalised Verhulst differential equations
Population dynamics

Access to Document

10.1007/978-3-031-68949-9_2

Cite this

Brilhante, M. F., Gomes, M. I., Mendonça, S., Pestana, D., & Pestana, P. (2025). Population growth and geometrically thinned extreme value theory. In L. Henriques-Rodrigues, R. Menezes, L. M. Machado, S. Faria, & M. D. Carvalho (Eds.), New frontiers in statistics and data science: SPE2023 (pp. 13-26). (Springer Proceedings in Mathematics and Statistics). Springer. https://doi.org/10.1007/978-3-031-68949-9_2

Brilhante, M. Fátima ; Gomes, M. Ivette ; Mendonça, Sandra et al. / Population growth and geometrically thinned extreme value theory. New frontiers in statistics and data science: SPE2023. editor / Lígia Henriques-Rodrigues ; Raquel Menezes ; Luís Meira Machado ; Susana Faria ; Miguel de Carvalho. Springer, 2025. pp. 13-26 (Springer Proceedings in Mathematics and Statistics).

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title = "Population growth and geometrically thinned extreme value theory",

abstract = "Starting from the simple Beta(2,2) model, connected to the Verhulst logistic parabola, several extensions are discussed, and connections to extremal models are revealed. Aside from the classical general extreme value model, extreme value models in randomly stopped extremes schemes are also discussed. Logistic and Gompertz growth equations are the usual choice to model sustainable growth. Therefore, observing that the logistic distribution is (geo)max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, other growth models, related to classical and to geometrically thinned extreme value theory are investigated.",

keywords = "BetaBoop random variables, Extreme value theory, Generalised Verhulst differential equations, Population dynamics",

author = "Brilhante, \{M. F{\'a}tima\} and Gomes, \{M. Ivette\} and Sandra Mendon{\c c}a and Dinis Pestana and Pedro Pestana",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 26th Congress of the Portuguese Statistical Society, SPE 2023 ; Conference date: 13-10-2021 Through 16-10-2021",

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language = "English",

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editor = "L{\'i}gia Henriques-Rodrigues and Raquel Menezes and Machado, \{Lu{\'i}s Meira\} and Susana Faria and Carvalho, \{Miguel de\}",

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Brilhante, MF, Gomes, MI, Mendonça, S, Pestana, D & Pestana, P 2025, Population growth and geometrically thinned extreme value theory. in L Henriques-Rodrigues, R Menezes, LM Machado, S Faria & MD Carvalho (eds), New frontiers in statistics and data science: SPE2023. Springer Proceedings in Mathematics and Statistics, Springer, pp. 13-26, 26th Congress of the Portuguese Statistical Society, SPE 2023, Evora, Portugal, 13/10/21. https://doi.org/10.1007/978-3-031-68949-9_2

Population growth and geometrically thinned extreme value theory. / Brilhante, M. Fátima; Gomes, M. Ivette; Mendonça, Sandra et al.
New frontiers in statistics and data science: SPE2023. ed. / Lígia Henriques-Rodrigues; Raquel Menezes; Luís Meira Machado; Susana Faria; Miguel de Carvalho. Springer, 2025. p. 13-26 (Springer Proceedings in Mathematics and Statistics).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Population growth and geometrically thinned extreme value theory

AU - Brilhante, M. Fátima

AU - Gomes, M. Ivette

AU - Mendonça, Sandra

AU - Pestana, Dinis

AU - Pestana, Pedro

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

PY - 2025/1

Y1 - 2025/1

N2 - Starting from the simple Beta(2,2) model, connected to the Verhulst logistic parabola, several extensions are discussed, and connections to extremal models are revealed. Aside from the classical general extreme value model, extreme value models in randomly stopped extremes schemes are also discussed. Logistic and Gompertz growth equations are the usual choice to model sustainable growth. Therefore, observing that the logistic distribution is (geo)max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, other growth models, related to classical and to geometrically thinned extreme value theory are investigated.

AB - Starting from the simple Beta(2,2) model, connected to the Verhulst logistic parabola, several extensions are discussed, and connections to extremal models are revealed. Aside from the classical general extreme value model, extreme value models in randomly stopped extremes schemes are also discussed. Logistic and Gompertz growth equations are the usual choice to model sustainable growth. Therefore, observing that the logistic distribution is (geo)max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, other growth models, related to classical and to geometrically thinned extreme value theory are investigated.

KW - BetaBoop random variables

KW - Extreme value theory

KW - Generalised Verhulst differential equations

KW - Population dynamics

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SN - 9783031726071

T3 - Springer Proceedings in Mathematics and Statistics

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BT - New frontiers in statistics and data science

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A2 - Menezes, Raquel

A2 - Machado, Luís Meira

A2 - Faria, Susana

A2 - Carvalho, Miguel de

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T2 - 26th Congress of the Portuguese Statistical Society, SPE 2023

Y2 - 13 October 2021 through 16 October 2021

ER -

Brilhante MF, Gomes MI, Mendonça S, Pestana D, Pestana P. Population growth and geometrically thinned extreme value theory. In Henriques-Rodrigues L, Menezes R, Machado LM, Faria S, Carvalho MD, editors, New frontiers in statistics and data science: SPE2023. Springer. 2025. p. 13-26. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-68949-9_2

Population growth and geometrically thinned extreme value theory

Abstract

Publication series

Conference

Keywords

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CITAR - Research Center for Science and Technology of the Arts: UID/622/2025. Pluriannual 2025-2029

Cite this

Population growth and geometrically thinned extreme value theory

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

CITAR - Research Center for Science and Technology of the Arts: UID/622/2025. Pluriannual 2025-2029

Cite this