Abstract:
Extreme events are defined as values of the event below or above a certain
value called threshold. A well chosen threshold helps to identify the extreme
levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the
maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks
down when there is a tie in the exceedances. This study offers a solution to
model data even if it contains ties. To do so, an optimal threshold that gives
more optimal parameters for extreme events, was determined. The study
achieved its main objective by deriving a method that improved MPS method
for determining an optimal threshold for extreme values in a data set containing ties, estimated the Generalized Pareto Distribution (GPD) parameters
for the optimal threshold derived and compared these GPD parameters with
GPD parameters determined through the standard MPS model. The study
improved maximum product of spacing method and used Generalized Pareto
Distribution (GPD) and Peak over threshold (POT) methods as the basis of
identifying extreme values. This study will help the statisticians in different
sectors of our economy to model extreme events involving ties. To statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting
the likelihood of an occurrence of the extreme event.
