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Title:	Partition entropy and chi-squared error: the improved MEMPHIS algorithm - Part I
Author:	Cubarsí Morera, Rafael; Alcobé López, Santiago
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. gAGE - Grup d'Astronomia i Geomàtica
Abstract:	The entropy of the population partition is studied as a function of the sampling parameter, so that within a particular interval of its graph, the plateau region, it is possible to get a stable estimation of the mixture parameters. The optimal estimation is associated with a local maximum of entropy. Alter natively, the $\chi^2$ error of the mixture approach may also be used to obtain an optimal segregation. The relationship between the fitting error and the population entropy has been analysed in detail. We have proved that, by using an appropriate sampling parameter, within a plateau region of the entropy graph, a local entropy maximum takes place simultaneously with a local minimum of the $\chi^2$ error. Therefore, the combined statistical method provides the best approximation mixture, as well as the less informative partiti on, to estimate the kinematic parameters of populations.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Mètodes estadístics -Astronomy and astrophysics -Probabilities ; Stochastic processes -Mathematical statistics -Astronomia ; Astrofísica -Probabilitats ; Processos estocàstics -Estadística matemàtica -85 ASTRONOMY AND ASTROPHYSICS -60 PROBABILITY THEORY AND STOCHASTIC PROCESSES -62 STATISTICS
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Draft Report
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