Formula for Skewness in Aggregate Claims Distribution

Discussion in 'SP8' started by Mendoza2909, Apr 13, 2017.

  1. Mendoza2909

    Mendoza2909 Member

    Hi,

    So I can use the formulas

    Skew(S) =λE(X^3) and
    Coeff(S) = Skew(S)/(V(S)^1.5)

    if N is ~ Po(λ).

    What are the formulas when N is not ~ Poisson? I'm sure I've missed it but yeah I can't find it anywhere. I also tried Ask Jeeves but no luck.
     
  2. Katherine Young

    Katherine Young ActEd Tutor Staff Member

    To find the skewness of S in the case where N is not Poisson, you would have to work from first principles, using the MGF. Let me assure you, it's not much fun. By an astonishing coincidence however, I happen to have the derivation for a compound negative binomial distribution to hand. Please find this attached.

    Your formula for the coefficient of skewness is a general result, it can be used for any random variable.
     

    Attached Files:

    vidhya36 likes this.
  3. Mendoza2909

    Mendoza2909 Member

    Thanks a lot Katherine. Hope you enjoyed the long weekend!
     
  4. SR1982

    SR1982 Member

  5. vidhya36

    vidhya36 Very Active Member

    Can you repost the attachment? I am trying to download but resulting in error.
     
  6. Darren Michaels

    Darren Michaels ActEd Tutor Staff Member

    Here you go.
     

    Attached Files:

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