SKEDSOFT

Six Sigma

a)    Cauchy distribution:

b)      Power law:

We have already defined discrete power law distributions.  We present here a continuous analog.  Our  starting  point  is  to  introduce  tail  probabilities  that  decay according  to  power  law:

FX(x) = 0, otherwise.  In  order  for  X to  be  a  continuous  random  variable,  FX cannot  have  a  jump  at  x = c,  and  we  therefore  need  β = cα.  The corresponding density is of the form

EXPECTED VALUES:

Similar  to  the  discrete  case,  given  a  continuous  random  variable  X with  PDF fX,  we  define