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Math Help - [SOLVED] generating functions

  1. #1
    helpme2007
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    [SOLVED] generating functions

    can someone pls tell me the steps or ideas or materials or hints on how to obtain the moment generating function,probability generating function,cumulant generating function and characteristic function of probability distributions e.g beta distribution etc
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by helpme2007 View Post
    can someone pls tell me the steps or ideas or materials or hints on how to obtain the moment generating function,probability generating function,cumulant generating function and characteristic function of probability distributions e.g beta distribution etc
    there are two ways:

    i. Type the relevant terms into wikipedia and perform the given operations

    ii. Get a suitable handbook in which they are tabulated (Abramowitz and
    Stegun is probably a good place to start.

    RonL
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  3. #3
    Newbie
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    Smile Nice textbook

    I like "Probability and Random Processes" by Grimmett and Stirzaker Clarendon press, Oxford, United Kindom. Lots of examples from different areas plus main ideas like moment generating functions, Laplace transform and Fourier.
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  4. #4
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    Smile Some examples

    Characteristic fcn is just probabilists fancy name for Fourier or Laplace transform or some discrete version of this. You use it to calc expected values. This is kind of basic idea. For details see Grimmett & Stirzaker, GS from now.

    Answer to your other questions can also be found in this book:

    Probability genr fcn used for non-negative RV say X is G(s)=E[s^X]. GS p.129

    Moment genr fcn M(t)= E[exp t*X] sort of like Laplace transform. You use it to find EX = M'(0) where prim means derivative of M at point t=0. Higher moments EX^k = M^k(0), derivative order k. GS p.162

    Cumulant generating fcn is the log of the moment generating fcn of RV say X.
    log E[exp theta*X]. GS p.166

    Good luck in calculating the char fcn for a RV with beta distribution..... Looks tough to me!
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