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Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times

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Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times

dc.contributor.author	Castro Palacio, Juan Carlos
dc.contributor.author	Isidro San Juan, José María
dc.contributor.author	Navarro Pardo, Esperanza
dc.contributor.author	Velázquez Abad, Luisberis
dc.contributor.author	Fernández de Córdoba, Pedro
dc.date.accessioned	2021-02-04T16:44:21Z
dc.date.available	2021-02-04T16:44:21Z
dc.date.issued	2021
dc.identifier.citation	Castro Palacio, Juan Carlos Isidro San Juan, José María Navarro Pardo, Esperanza Velázquez Abad, Luisberis Fernández de Córdoba, Pedro 2021 Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times Mathematics 9 77
dc.identifier.uri	https://hdl.handle.net/10550/77602
dc.description.abstract	The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution we will still represent approximately in terms of a Chi distribution. We perform a Monte Carlo simulation to generate a random variable which is obtained from the positive square root of the sum of k squared variables, but this time coming from non-standard Normal distributions, where the variances can take any positive value. Then, we determine the boundaries of what to expect when we start from a set of unequal variances in the generating Gaussians. In the second part of the article, we present a discrete model to calculate the parameter of the Chi distribution in an approximate way for this case (unequal variances). We also comment on the application of this simple discrete model to calculate the parameter of the MB distribution (Chi of k = 3) when it is used to represent the reaction times to visual stimuli of a collective of individuals in the framework of a Physics inspired model we have published in a previous work.
dc.language.iso	eng
dc.relation.ispartof	Mathematics, 2021, vol. 9, p. 77
dc.subject	Psicologia
dc.title	Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times
dc.type	journal article	es_ES
dc.date.updated	2021-02-04T16:44:21Z
dc.identifier.doi	10.3390/math9010077
dc.identifier.idgrec	143152
dc.rights.accessRights	open access	es_ES