Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.11.2001.tde-26032002-113122
Document
Auteur
Nom complet
Denise Nunes Viola
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
Piracicaba, 2001
Directeur
Jury
Corrente, Jose Eduardo (Président)
Barreto, Maria Cecilia Mendes
Demetrio, Clarice Garcia Borges
Titre en portugais
Redução no vício da distribuição da deviance para dados de contagem.
Mots-clés en portugais
desvio
distribuição de Poisson
série de Taylor
Resumé en portugais
Titre en anglais
Bias reduction in the distribution of the deviance for count data.
Mots-clés en anglais
deviance
Poisson distribution
Taylor series
Resumé en anglais
Analysis of count data presents, in general, can be supposed coming from a Poisson distribution. The analysis of such data have some problems once the underlying distribution of them does not follow the basic assumptions to fit a model. Some tranformations can be suggested, but good results are not always obtained. In the approach of the Generalized Linear Models, the deviance is the statistics that measures the goodness of fit, but its distribution is unknown. Furthermore, considering Poisson distribution data, it is possible to approximate the distribution of the deviance for a chi-square distribution, but such approximation is not good for small sample size. In order of improve this approximation, corrections for the data are suggested, but the results are not good yet. Then, the aim of this work is to propose a new correction factor for data following a Poisson distribution in order to obtain an improvement in the distribution of the deviance for any sample size. For this, just adding a constant at the response variable and, through the expected value of the deviance, such constant is obtained in order to reduce the error in the aproximation. Simulated data from the Poisson distribution were made to calculate the deviance with and without the correction and QQ-plots were used to compare the values of the deviance with the chi-square distribution.

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Date de Publication
2002-04-08

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