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       #Post#: 56--------------------------------------------------
       Inverse CDF of Discrete Distribution (HW5 Q1.2)
       By: Matt Dolin Date: February 25, 2023, 2:50 pm
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       I am somewhat confused about how to calculate the inverse CDF of
       a discrete distribution. Could the inverse CDF of a Poisson
       distribution be calculated as the inverse of a normal
       distribution which approximates the Poisson distribution? Or is
       there a better method for approximating which amount of Poisson
       trials would produce a certain probability of success? Thank
       you!
       #Post#: 57--------------------------------------------------
       Re: Inverse CDF of Discrete Distribution (HW5 Q1.2)
       By: Taeho Kim Date: February 25, 2023, 4:36 pm
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       Hi Matt,
       Yes, the discrete case of the inverse transformation method can
       be confusing.
       The reason is that while the idea uses the inverse CDF,
       we actually don't need to do the actual inversion for the
       implementation.
       See the generation scheme on page 18 of Generating Random
       Variable I
  HTML https://drive.google.com/file/d/1Zu5pZbXNXwPz_yyl8F4UJ6mtSTxA3vRG/view.
       The algorithm does not use inverse CDF anywhere.
       What we need to do is:
       [list type=decimal]
       [li]Find out the CDF values at the discontinuity points (in this
       case 0,1,2,3,...), and
       chop the interval (0,1) with those CDF values;[/li]
       [li]Generate u from uniform(0,1);[/li]
       [li]Track which sub-interval u falls into so that we can assign
       new random variables accordingly.[/li]
       [/list]
       This procedure is actually what we did in our lab 9.
       The sample code for logarithm distribution (we saw this on
       Tuesday) would be helpful
       since the Poisson distribution is somewhat similar to the
       "logarithm" distribution (Both have infinite discontinuities.)
       Please let me know if you need further clarification.
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