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Thread: Continuity correction, poisson

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    Continuity correction, poisson




    Hi

    There is something that puzzles me. I tried calculating a Poisson probability. Exactly, and with the normal distribution, using both the continuity and without the continuity correction. However the answer became much more exact if I did it not using continuity correction, do you see why?

    It is a poisson distribution with parameter \lambda=168.
    I want to calculate P(X \ge 196).

    I get that the exact answer is:
    0.01876504
    The answer using CLT and continuity correction :0.01693269
    And without the continuity correction I get: 0.01862127

    R-code:
    Code: 
    1-ppois(195,168) #exact
    1-pnorm((195.5-168)/sqrt(168)) #with correction
    1-pnorm((195-168)/sqrt(168))   #without correction
    Do you see why in this case it is best to not use continuity correction?

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    Re: Continuity correction, poisson

    Your "without correction" method isn't actually correct. If you were to go without a correction you would just look at the area greater than or equal to 196 (exactly what the probability statement says).

    Code: 
    > 1-ppois(195,168) #exact
    [1] 0.01876504
    > 1-pnorm((195.5-168)/sqrt(168)) #with correction
    [1] 0.01693269
    > 1-pnorm((196-168)/sqrt(168)) #without correction
    [1] 0.01537678
    So the correction is helping.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Continuity correction, poisson

    Quote Originally Posted by Dason View Post
    Your "without correction" method isn't actually correct. If you were to go without a correction you would just look at the area greater than or equal to 196 (exactly what the probability statement says).

    Code: 
    > 1-ppois(195,168) #exact
    [1] 0.01876504
    > 1-pnorm((195.5-168)/sqrt(168)) #with correction
    [1] 0.01693269
    > 1-pnorm((196-168)/sqrt(168)) #without correction
    [1] 0.01537678
    So the correction is helping.
    I got 195 using this:

    P(X \ge 196)=1-P(X <195)=1-P(\frac{X-168}{\sqrt{168}}<\frac{195-168}{\sqrt{168}})
    \approx P(Z<\frac{195-168}{\sqrt{168}})

    Did I do a mistake somewhere?

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    Re: Continuity correction, poisson


    You have a mistake on your first equality: It should be P(X >= 196) = 1 - P(X < 196).

    But that doesn't matter - you're bringing in the discrete nature of the poisson too soon. Remember what you're doing here. You'll applying the CLT. So you're saying that you think your random variable is approximately normally distributed and you know that the mean is 168 and the variance is also 168.

    So if I tell you that you have a normal random variable with a mean and variance of 168 and ask you to find P(X >= 196) what would you do? Ignore everything else - just use the fact that you have a random variable that you think is normal and you know the mean and the variance.
    I don't have emotions and sometimes that makes me very sad.

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