Huberized: Detecting Outliers in Circular Data and Modifying Its

Description

This function is used to identify outliers in circular data sets. and with do the procedure Huberized on this outliers, the results improve. Huberizing the outliers will improve the results. circular and sd.circular are mean and standard deviation of circular data.

Usage

Huberized(t)

Arguments

circular data set which contains suspected outliers.

Value

plot1: plot data set when exist outlier.
plot2: plot data set after modified outlier.
m: mean.circular when exist outlier.
m1: mean.circular after modified outlier.
s: sd.circular when exist outlier.
s1: sd.circular after modified outlier.

Details

In this method, we progressively transform the original data by a process called winsorisation. Assume that we have initial estimates called m,s. (These coulde evaluated as mean and standard deviation.) If a value $x_i$ falls above m+(1.5*s) then we change it to $x_i=m+(1.5*s)$. Likewise if a value falls below m-(1.5*s) then we change it to $x_i=m=(1.5*s)$. We then calculate an improved estimate of mean as m1=mean.circular($x_i$), and of the standard deviation as s1=1.134*(sd.circular($x_i$)).(The factor 1.134 is derived from the normal distribution, given a value 1.5 for the multiplier most often used in the winsorisation process.) (see the first reference)

References

Analytical Methods Committe, Robust statistics: a method coping with outliers, Royal Society of Chemistry 2001, amc technical brief.

A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detecting of outliers in simple circular regression models using the mean circular error statistics.

Examples

Run this code

data(wind)
Huberized(wind)

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