The Role of Asymmetric Families of Distributions in Eliminating Risk
Modeling is always a crucial component of the risk assessment process. The use of adequate classes of distributions to model real data sets seems sensible to accommodate specific peculiarities of the data and enable us to implement resistant procedures, less sensitive to changes in the model. Despite the practical advantages of using the normal distribution, it is recognized that most of the data from diverse areas of application, such as economics, environment, finance, insurance, meteorology, reliability and statistical quality control, among others, usually exhibit moderate to strong asymmetry and heavier tails than the normal tail. This study motivates the use of two classes of skew-normal distributions that include highly skewed and heavy-tailed distributions as well as models that are close to the Gaussian family. Some guidelines for inference on the parameters of the model are suggested, and applications to real data sets are presented.
KeywordsAsymmetric families of distributions Control charts Data modeling Skew-normal SPC
Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, projects PEst-OE/MAT/UI0006/2014, PEst-OE /MAT /UI0006 /2011 (CEAUL) and EXTREMA, PTDC /MAT /101736 /2008. The authors would like to acknowledge the helpful suggestions of the anonymous reviewers and the editor.
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