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.
Highlights
Certain values in the tails of any distribution, represent extreme events and they are pointers to eventuality
The study achieved its main objective by deriving a method that improved maximum product of spacing (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 improved MPS, both two-parameter and three-parameter models yielded a higher threshold as compared to the two standard MPS model Table 1 and Table 2
Summary
Certain values in the tails of any distribution, represent extreme events and they are pointers to eventuality. By taking all exceedances over a suitably high threshold into account, they use the data more efficiently and second, they are extended to situations where one wants to study how the extreme levels of a variable Y depend on some other variable X for instance, Y may be the level of tropospheric ozone on a particular day and X a vector of meteorological variables for that day. This kind of problem is almost impossible to handle through the annual maxima/minima method.
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