1. Posts in the subject areas are now being moderated. Please do not post any details about your exam for at least 3 working days. You may not see your post appear for a day or two. See the 'Forum help' thread entitled 'Using forums during exam period' for further information. Wishing you the best of luck with your exams.
    Dismiss Notice

SP9 M16 pg13 error in Leptokurtic graph

Discussion in 'SP9' started by Johann, May 21, 2019.

Tags:
  1. Johann

    Johann Member

    Hi All,
    Just a quick question, I think the solution to the question on pg16 of Module 16 is showing the wrong distribution to be Leptokurtic (i.e. it is showing the t-distn with gamma = 1) from my understanding this should be platykurtic compared to the standard normal distribution. Is this correct or am i missing something?

    Thanks
    Johann
     
    Johann, May 21, 2019
    #1
  2. Anna Bishop

    Anna Bishop ActEd Tutor Staff Member

    Hello Johann

    Just had a quick look at Sweeting P157/158 and think the graph is OK. When gamma = 1 we have the Cauchy distribution, which is renowned for its fat tails (leptokurtic).

    I also tried a sense check with the PDF on P157 of Sweeting, putting in gamma = 1. I get:

    f(x) = (1/β pi) {1 + [(x-α)/β]^2}^-1

    This looks like it has power decay (heavier tails) whereas the normal distribution has exponential decay (lighter tails).

    Is this OK?
    Anna
     
    Anna Bishop, May 21, 2019
    #2
  3. Johann

    Johann Member

    Okay thank you for this Anna, so just to confirm (heavier tails/leptokurtic) distributions produces more extreme events than the (lighter tails/platykurtic) distributions? Think I may have been missing this point?
     
    Johann, May 22, 2019
    #3
  4. Anna Bishop

    Anna Bishop ActEd Tutor Staff Member

    Hi Johann, yes, leptokurtic distributions typically have a fatter tailed / thinner peaked PDF than a normal distribution would have. This means that it assigns higher probabilities to extreme events.
     
    Anna Bishop, May 22, 2019
    #4
  5. Johann

    Johann Member

    Perfect, thanks :)
     
    Johann, May 23, 2019
    #5

Share This Page