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    Question Poisson curve for low lambda




    Hello,

    I'm quite new to probability and currently trying to understand the different distributions.

    I see the Poisson curve is weirdly shaped for law lambda values, and I'm wondering if it is reliable in real world examples? Intuitively I would say it is flawed when I try following examples:
    - I expect 1 meteor to hit the earth per hour, so λ=1. The probability that no meteor hits the earth in a specific (and thus every hour) is exactly as big as that 1 meteor will hit.
    - I expect 4 meteors to hit the earth per hour, so λ=4. The probability that 3 meteors hit is exactly the same as 4.

    Is this something that is generally accepted, or is it not wise to use poisson for these kind of probability tests?

    Kind regards
    Sam

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    Re: Poisson curve for low lambda

    ... yes that's the way the Poisson distribution works. I don't understand what your objection is.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Poisson curve for low lambda

    I'm just trying to understand how this could ever give a correct probability for real world data. And if it does not, whether people using this distribution are avoiding this 'issue' or coping with this in any way?

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    Re: Poisson curve for low lambda

    The poisson distribution can be used to approximate a binomial probability. It's useful when you have a very large sample size and a small success probability. In fact, the poisson formula is derived from the binomial formula.
    "I have discovered a truly remarkable proof of this theorem which this margin is too narrow to contain." Pierre de Fermat

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    Re: Poisson curve for low lambda

    You still haven't actually pointed out what you think the issue is. You've stated facts about the distribution. Facts that are true and make sense for some real world data. What is your objection. Why do you think these things aren't accurate.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Poisson curve for low lambda

    Ok, let me give it a try

    Suppose my second example where we know there are on average 4 meteors per hour. This makes on average 96 per day.

    I'm doing a money game against a friend to guess the number of hits for every elapsed hour. Now using the Poisson probability function, for every hour of the day I check the most likely number of hits. It is 19.5% for both 3 and 4 hits. Since the odds are as likely, my bet for the first hour would be 3 hits, and for the second hour 4 hits. I will alternate like this for the remainder of the day.
    When I calculate how many hits I estimated, it sums up to 84. My friend (who says Poisson is a waste of time) just guessed the average number 4 each time. At the end of the day he estimated 96 total meteor hits.
    How likely am I to win the money pot?

    Please note though I'm not trying to break this model but rather want to understand why the issue I'm seeing is not an issue.

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    Re: Poisson curve for low lambda


    So, your basically asking why the probability for 3 hits is almost identical to the probability for 4 hits? Furthermore, why bother to compute it if it is almost identical? I'll leave that one for Dason to answer.
    Last edited by Buckeye; 08-12-2016 at 10:46 AM.
    "I have discovered a truly remarkable proof of this theorem which this margin is too narrow to contain." Pierre de Fermat

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