KendalTauCoefficient
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Function Description
Returns the Kendal’s
Tau  between two series,
 between two series,  and
 and  .
.
 
If  are a set of joint
observations from two random variables
are a set of joint
observations from two random variables  and
 and  then
pairs
 then
pairs  and
 and  
  are
said to be ‘concordant’ if both
 are
said to be ‘concordant’ if both  and
 and  (or if both
 (or if both  and
 and  ). They are said to be
‘discordant’ if
). They are said to be
‘discordant’ if  and
 and  or if
 or if  and
 and  . Then the elements of
the matrix are as follows, where each entry separately considers all possible
pairs of
. Then the elements of
the matrix are as follows, where each entry separately considers all possible
pairs of  for
 for  ,
,  and
 and 
 

 
N.B. There are various possible approaches to ties. The one
implemented here reduces the denominator so that we still have  and
in the presence of ties,
 and
in the presence of ties,  can take either extreme
value in some circumstances.
 can take either extreme
value in some circumstances.
 
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