Doctoral Thesis
DOI
10.11606/T.17.2017.tde-06062017-170620
Document
Author
Full name
Davi Casale Aragon
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Ribeirão Preto, 2016
Supervisor
Committee
Martinez, Edson Zangiacomi (President)
Cupo, Palmira
Passos, Afonso Dinis Costa
Souza, Eniuce Menezes de
Title in Portuguese
Modelos de séries temporais de dados de contagem baseados na distribuição Poisson Dupla
Keywords in Portuguese
M´etodos Bayesianos
Poisson Dupla
S´eries Temporais
Abstract in Portuguese
Title in English
Count data time series models based on Double Poisson distribution
Keywords in English
Bayesian Methods
Double Poisson
Time Series
Abstract in English
Time series data are derived from studies in which there are reported mortality, number of hospitalizations infections by disease or other event of interest per day, week, month or year, in order to observe trends, seasonality or associated factors. Count data are represented by discrete quantitative variables, i.e. observations that take integer values in the range {0, 1, 2, 3, ...}. In view of this particular characteristic, such data must be analyzed by adequate statistical tools and the Poisson distribution is an option for modeling, being more suitable than models based on methods proposed by Box and Jenkins (2008), usually applied for continuous data, but used in the modeling of discrete data after logarithmic transformation. A limitation of the Poisson distribution is that it assumes equal mean and variance being an obstacle in cases which there are data overdispersion (variance higher than mean) or underdispersion (variance lower than mean). Therefore the Double Poisson distribution, proposed by Efron (1986), is an alternative because it allows to estimate the mean and variance parameters in cases wich variance of the data is lower, equal, or higher than mean providing great flexibility to the models. This work aims to develop time series models for count data, under Bayesian approach using probability distributions for discrete variables such as Poisson and Double Poisson. Furthermore it will be introduced a zero-inflated Double Poisson model to excess zeros counting data. The results obtained by adjusting the time series models based on Double Poisson distribution are compared with those obtained by considering the Poisson distribution. As main applications modeling of snake bites reports in the State of S~ao Paulo and scorpion stings in the city of Ribeir~ao Preto considering covariates as maximum and minimum average monthly temperatures and rainfall among the years 2007 and 2014 will be presented. Regression models based on double Poisson distribution showed a better fit to the data, when compared to Poisson models.