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Analysis of supermarket sales data using independent mixture and hidden Markov models
(06/29/2018) Asimaki, Kyriaki; Ασημάκη, Κυριακή; Kyriakidis, Epaminondas; Psarakis, Stelios; Athens University of Economics and Business, Department of Statistics; Besbeas, Panagiotis
This thesis deals with unbounded count data. The most common distribution for modeling such data is the Poisson distribution. However, in many real-world situations the sample variance is greater than the sample mean and observations are dependent like the data set which we analyze, namely weekly soap sales. First to deal with these problems, we use independent mixture models with Poisson, negative binomial and combinations of Poisson and negative binomial components which we term hybrid models. We demonstrate standard error and confidence interval estimation from hybrid models using asymptotic theory. Subsequently, we use Poisson and negative binomial hidden Markov models. These models are a popular approach for modeling sequential data and are based on Markov chain assumptions of a first or higher-order.Lastly, we compare results and demonstrate standard error estimation of hidden Markov models which are selected and corresponding confidence intervals with the bootstrap method.