The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy

Novel measures of symbol dominance (dC1 and dC2), symbol diversity (DC1 = N (1 - dC1) and DC2 = N (1 - dC2)), and information entropy (HC1 = log2 DC1 and HC2 = log2 DC2) are derived from Lorenz-consistent statistics that I had previously proposed to quantify dominance and diversity in ecology. Here,...

Descripción completa

Detalles Bibliográficos
Autor: Camargo Benjumeda, Julio Alfonso
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/47229
Acceso en línea:http://hdl.handle.net/10017/47229
https://dx.doi.org/10.3390/e22050542
Access Level:acceso abierto
Palabra clave:Camargo statistics
Lorenz curve
Rényi´s entropy
Shannon´s entropy
Information entropy
Symbol diversity
Symbol dominance
Medio Ambiente
Environmental science
id ES_bfd72e9ae39667e0725e181c0ef8dc2a
oai_identifier_str oai:ebuah.uah.es:10017/47229
network_acronym_str ES
network_name_str España
repository_id_str
spelling The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information EntropyCamargo Benjumeda, Julio AlfonsoCamargo statisticsLorenz curveRényi´s entropyShannon´s entropyInformation entropySymbol diversitySymbol dominanceMedio AmbienteEnvironmental scienceNovel measures of symbol dominance (dC1 and dC2), symbol diversity (DC1 = N (1 - dC1) and DC2 = N (1 - dC2)), and information entropy (HC1 = log2 DC1 and HC2 = log2 DC2) are derived from Lorenz-consistent statistics that I had previously proposed to quantify dominance and diversity in ecology. Here, dC1 refers to the average absolute difference between the relative abundances of dominant and subordinate symbols, with its value being equivalent to the maximum vertical distance from the Lorenz curve to the 45-degree line of equiprobability; dC2 refers to the average absolute difference between all pairs of relative symbol abundances, with its value being equivalent to twice the area between the Lorenz curve and the 45-degree line of equiprobability; N is the number of different symbols or maximum expected diversity. These Lorenz-consistent statistics are compared with statistics based on Shannon's entropy and Rényi's second-order entropy to show that the former have better mathematical behavior than the latter. The use of dC1, DC1, and HC1 is particularly recommended, as only changes in the allocation of relative abundance between dominant (pd > 1/N) and subordinate (ps < 1/N) symbols are of real relevance for probability distributions to achieve the reference distribution (pi = 1/N) or to deviate from it.Universidad de Alcalá20202020-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/47229https://dx.doi.org/10.3390/e22050542reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengUAH Not available MC-100open accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/472292026-06-18T11:13:07Z
dc.title.none.fl_str_mv The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
title The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
spellingShingle The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
Camargo Benjumeda, Julio Alfonso
Camargo statistics
Lorenz curve
Rényi´s entropy
Shannon´s entropy
Information entropy
Symbol diversity
Symbol dominance
Medio Ambiente
Environmental science
title_short The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
title_full The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
title_fullStr The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
title_full_unstemmed The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
title_sort The Lorenz Curve: A Proper Framework to Define Satisfactory Measures of Symbol Dominance, Symbol Diversity, and Information Entropy
dc.creator.none.fl_str_mv Camargo Benjumeda, Julio Alfonso
author Camargo Benjumeda, Julio Alfonso
author_facet Camargo Benjumeda, Julio Alfonso
author_role author
dc.subject.none.fl_str_mv Camargo statistics
Lorenz curve
Rényi´s entropy
Shannon´s entropy
Information entropy
Symbol diversity
Symbol dominance
Medio Ambiente
Environmental science
topic Camargo statistics
Lorenz curve
Rényi´s entropy
Shannon´s entropy
Information entropy
Symbol diversity
Symbol dominance
Medio Ambiente
Environmental science
description Novel measures of symbol dominance (dC1 and dC2), symbol diversity (DC1 = N (1 - dC1) and DC2 = N (1 - dC2)), and information entropy (HC1 = log2 DC1 and HC2 = log2 DC2) are derived from Lorenz-consistent statistics that I had previously proposed to quantify dominance and diversity in ecology. Here, dC1 refers to the average absolute difference between the relative abundances of dominant and subordinate symbols, with its value being equivalent to the maximum vertical distance from the Lorenz curve to the 45-degree line of equiprobability; dC2 refers to the average absolute difference between all pairs of relative symbol abundances, with its value being equivalent to twice the area between the Lorenz curve and the 45-degree line of equiprobability; N is the number of different symbols or maximum expected diversity. These Lorenz-consistent statistics are compared with statistics based on Shannon's entropy and Rényi's second-order entropy to show that the former have better mathematical behavior than the latter. The use of dC1, DC1, and HC1 is particularly recommended, as only changes in the allocation of relative abundance between dominant (pd > 1/N) and subordinate (ps < 1/N) symbols are of real relevance for probability distributions to achieve the reference distribution (pi = 1/N) or to deviate from it.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/47229
https://dx.doi.org/10.3390/e22050542
url http://hdl.handle.net/10017/47229
https://dx.doi.org/10.3390/e22050542
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv UAH Not available MC-100
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869418425900597248
score 15,300719

Similares en LA Referencia