Functional extreme data analysis methods and its application to rainfall data

Functional data analysis is one of the new techniques to transform a discrete or continuous observation into a functional form. Conventional classical statistics methods now can be observed and analyzed through a curve for almost all types of data with neither distribution assumption nor goodness of fit test that are necessary to be followed. Literature reviews show that there is no study found for functional data analysis application on extreme data which deals with maximum value in the data set. In this thesis, the study has extended the functional data analysis methodology to cover on extreme data with several substitution methods have been introduced. Some characteristics of functional extreme data analysis such as on environmental data are explained. The tolerance bands for functional mean extreme data is proposed using bootstrapping method by implementing the percentile computation in determining the upper and lower limits of the mean function. The performance of the functional extreme data analysis is carried out. The equal and unequal space of time cases are considered to be implemented for the functional extreme data. The study found that only data that consists a large number of extreme data will be performed in functional extreme data for unequal space of time. Otherwise, a small number of extreme data is suggested to use the equal space of time to obtain a smooth curve.

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