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Q&A4 Q4.11c

Discussion in 'SP9' started by ALEX_AK, May 1, 2018.

  1. ALEX_AK

    ALEX_AK Member

    We can derive the mean excess from the pdf, 1/(b-u).
    This is a uniform distribution with parameters b and u.
    Hence mean = 1/2*(b+u)
    As u increase, mean increase.
    The answer to this question mention that mean excess will decrease linearly. This part seems to contradict what I have derived as above.
    Anyone knows the explanation for this?
     
    ALEX_AK, May 1, 2018
    #1
  2. Simon James

    Simon James ActEd Tutor Staff Member

    Hi. I think the XS distribution (ie Y=X-u) is uniform U(0,b-u) not (u,b).

    So, you end up with mean of (b-u)/2 as expected.

    Intuitively this must be true. As u increases the distance to b decreases, so the average distance to b decreases (note that the mean of the losses > u does increase. The mean of the losses > u is (b+u)/2, but as we are interested in the excess loss, we have (b+u)/2-u)
     
    Last edited: May 1, 2018
    Simon James, May 1, 2018
    #2
    ALEX_AK likes this.
  3. ALEX_AK

    ALEX_AK Member

    Thanks a lot for the explanation.
     
    ALEX_AK, May 5, 2018
    #3

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