This HTML5 document contains 53 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
dbpedia-eshttp://es.dbpedia.org/resource/
n17https://global.dbpedia.org/id/
yagohttp://dbpedia.org/class/yago/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
n13http://www.hubbertpeak.com/laherrere/
freebasehttp://rdf.freebase.com/ns/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
dbpedia-frhttp://fr.dbpedia.org/resource/
wikipedia-enhttp://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
dbchttp://dbpedia.org/resource/Category:
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
goldhttp://purl.org/linguistics/gold/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:List_of_probability_distributions
dbo:wikiPageWikiLink
dbr:Parabolic_fractal_distribution
Subject Item
dbr:Zipf's_law
dbo:wikiPageWikiLink
dbr:Parabolic_fractal_distribution
Subject Item
dbr:History_of_statistics
dbo:wikiPageWikiLink
dbr:Parabolic_fractal_distribution
Subject Item
dbr:King_effect
dbo:wikiPageWikiLink
dbr:Parabolic_fractal_distribution
Subject Item
dbr:List_of_statistics_articles
dbo:wikiPageWikiLink
dbr:Parabolic_fractal_distribution
Subject Item
dbr:Parabolic_fractal_distribution
rdf:type
yago:PsychologicalFeature100023100 yago:Structure105726345 yago:WikicatProbabilityDistributions yago:Cognition100023271 yago:WikicatDiscreteDistributions yago:Distribution105729036 yago:Abstraction100002137 dbo:Software yago:Arrangement105726596
rdfs:label
Distribución fractal parabólica Parabolic fractal distribution Loi fractale parabolique
rdfs:comment
En probabilidad y estadística, la distribución fractal parabólica es un tipo de distribución de probabilidad discreta en la que el logaritmo de la frecuencia o el tamaño de las entidades en una población es un polinomio cuadrático del logaritmo de la fila. Esto puede mejorar notablemente el ajuste a través de una sencilla relación de ley de potencia (ver referencias más abajo). En una serie de aplicaciones, hay un llamado efecto rey, por el que el elemento de más alto rango tiene una frecuencia o tamaño significativamente mayor que el que el modelo predice sobre la base de los otros artículos. En théorie des probabilités et en statistique, une distribution fractale parabolique est une loi de probabilité discrète pour laquelle le logarithme de la fréquence (ou la taille) des classes dans une population s'exprime comme une fonction du second degré du logarithme du rang. Ces lois permettent d'améliorer notablement la qualité de la régression par rapport à une simple relation sous la forme d'une fonction puissance. In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (with the largest example having rank 1). This can markedly improve the fit over a simple power-law relationship (see references below). 1. * Paris, 12.09M 2. * Lyon, 2.12M 3. * Marseille, 1.72M 4. * Toulouse, 1.20M 5. * Lille, 1.15M
dcterms:subject
dbc:Discrete_distributions
dbo:wikiPageID
1096151
dbo:wikiPageRevisionID
992710906
dbo:wikiPageWikiLink
dbr:Quadratic_polynomial dbr:Overfitting dbc:Discrete_distributions dbr:Discrete_probability_distribution dbr:Probability dbr:King_effect dbr:Probability_mass_function dbr:Statistics dbr:Comptes_rendus_de_l'Académie_des_sciences dbr:Parabola dbr:Zipf's_law
dbo:wikiPageExternalLink
n13:fractal.htm n13:fractal.htm)
owl:sameAs
wikidata:Q3258499 freebase:m.045nhy n17:313go dbpedia-fr:Loi_fractale_parabolique dbpedia-es:Distribución_fractal_parabólica yago-res:Parabolic_fractal_distribution
dbp:wikiPageUsesTemplate
dbt:Cite_journal dbt:ProbDistributions
dbo:abstract
En théorie des probabilités et en statistique, une distribution fractale parabolique est une loi de probabilité discrète pour laquelle le logarithme de la fréquence (ou la taille) des classes dans une population s'exprime comme une fonction du second degré du logarithme du rang. Ces lois permettent d'améliorer notablement la qualité de la régression par rapport à une simple relation sous la forme d'une fonction puissance. Dans de nombreuses applications, la classe du premier rang a une fréquence ou taille plus élevée que celle que prédit le modèle fondé sur les autres classes. Cet effet est appelé l'effet roi ou King effect. En probabilidad y estadística, la distribución fractal parabólica es un tipo de distribución de probabilidad discreta en la que el logaritmo de la frecuencia o el tamaño de las entidades en una población es un polinomio cuadrático del logaritmo de la fila. Esto puede mejorar notablemente el ajuste a través de una sencilla relación de ley de potencia (ver referencias más abajo). En una serie de aplicaciones, hay un llamado efecto rey, por el que el elemento de más alto rango tiene una frecuencia o tamaño significativamente mayor que el que el modelo predice sobre la base de los otros artículos. In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (with the largest example having rank 1). This can markedly improve the fit over a simple power-law relationship (see references below). In the Laherrère/Deheuvels paper below, examples include galaxy sizes (ordered by luminosity), towns (in the USA, France, and world), spoken languages (by number of speakers) in the world, and oil fields in the world (by size). They also mention utility for this distribution in fitting seismic events (no example). The authors assert the advantage of this distribution is that it can be fitted using the largest known examples of the population being modeled, which are often readily available and complete, then the fitted parameters found can be used to compute the size of the entire population. So, for example, the populations of the hundred largest cities on the planet can be sorted and fitted, and the parameters found used to extrapolate to the smallest villages, to estimate the population of the planet. Another example is estimating total world oil reserves using the largest fields. In a number of applications, there is a so-called King effect where the top-ranked item(s) have a significantly greater frequency or size than the model predicts on the basis of the other items. The Laherrère/Deheuvels paper shows the example of Paris, when sorting the sizes of towns in France. When the paper was written Paris was the largest city with about ten million inhabitants, but the next largest town had only about 1.5 million. Towns in France excluding Paris closely follow a parabolic distribution, well enough that the 56 largest gave a very good estimate of the population of the country. But that distribution would predict the largest city to have about two million inhabitants, not 10 million. The King Effect is named after the notion that a King must defeat all rivals for the throne and takes their wealth, estates and power, thereby creating a buffer between himself and the next-richest of his subjects. That specific effect (intentionally created) may apply to corporate sizes, where the largest businesses use their wealth to buy up smaller rivals. Absent intent, the King Effect may occur as a result of some persistent growth advantage due to scale, or to some unique advantage. Larger cities are more efficient connectors of people, talent and other resources. Unique advantages might include being a port city, or a Capital city where law is made, or a center of activity where physical proximity increases opportunity and creates a feedback loop. An example is the motion picture industry; where actors, writers and other workers move to where the most studios are, and new studios are founded in the same place because that is where the most talent resides. To test for the King Effect, the distribution must be fitted excluding the 'k' top-ranked items, but without assigning new rank numbers to the remaining members of the population. For example, in France the ranks are (as of 2010): 1. * Paris, 12.09M 2. * Lyon, 2.12M 3. * Marseille, 1.72M 4. * Toulouse, 1.20M 5. * Lille, 1.15M A fitting algorithm would process pairs {(1,12.09), (2,2.12), (3,1.72), (4,1.20), (5,1.15)} and find the parameters for the best parabolic fit through those points. To test for the King Effect we just exclude the first pair (or first 'k' pairs), and find parabolic parameters that fit the remainder of the points. So for France we wouldfit the four points {(2,2.12), (3,1.72), (4,1.20), (5,1.15)}. Then we can use those parameters to estimate the size of cities ranked [1,k] and determine if they are King Effect members or normal members. By comparison, Zipf's law fits a line through the points (also using the log of the rank and log of the value). A parabola (with one more parameter) will fit better, but far from the vertex the parabola is also nearly linear. Thus, although it is a judgment call for the statistician, if the fitted parameters put the vertex far from the points fitted, or if the parabolic curve is not a significantly better fit than a line, those may be symptomatic of overfitting (aka over-parameterization). The line (with two parameters instead of three) is probably the better generalization. More parameters always fit better, but at the cost of adding unexplained parameters or unwarranted assumptions (such as the assumption that a slight parabolic curve is a more appropriate model than a line). Alternatively, it is possible to force the fitted parabola to have its vertex at the rank 1 position. In that case, it is not certain the parabola will fit better (have less error) than a straight line; and the choice might be made between the two based on which has the least error.
gold:hypernym
dbr:Distribution
prov:wasDerivedFrom
wikipedia-en:Parabolic_fractal_distribution?oldid=992710906&ns=0
dbo:wikiPageLength
6088
foaf:isPrimaryTopicOf
wikipedia-en:Parabolic_fractal_distribution
Subject Item
dbr:Rank–size_distribution
dbo:wikiPageWikiLink
dbr:Parabolic_fractal_distribution
Subject Item
wikipedia-en:Parabolic_fractal_distribution
foaf:primaryTopic
dbr:Parabolic_fractal_distribution