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Math Help - Approximate with a Normal distribution (Bayesian statistics)

  1. #1
    Junior Member
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    Approximate with a Normal distribution (Bayesian statistics)

    Dear users,

    I am solving an exercise.
    Here, assume a Gamma distribution with a parameter lambda I have a priori:
    Pr(lambda is (belongs) [10,20])=0.95

    I have to approximate the priori with a Normal distribution.

    When I saw the solution, it says:

    after approximation with a normal distribution, we obtain the confidence interval: lambda belongs [15+-5]
    Which results in:
    E[lambda]=15
    V[lambda]=(5/1.96)^2=6.5.

    Please, could you explain me, how to approximate with a Normal distribution. And could you give me the formula itself. I cannot understand how to get the confidence interval [15+-5].

    What about the mean and the variance, I understood.

    Thank you in advance, I highly appreciate.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by JrShohin View Post
    Dear users,

    I am solving an exercise.
    Here, assume a Gamma distribution with a parameter lambda I have a priori:
    Pr(lambda is (belongs) [10,20])=0.95

    I have to approximate the priori with a Normal distribution.

    When I saw the solution, it says:

    after approximation with a normal distribution, we obtain the confidence interval: lambda belongs [15+-5]
    Which results in:
    E[lambda]=15
    V[lambda]=(5/1.96)^2=6.5.

    Please, could you explain me, how to approximate with a Normal distribution. And could you give me the formula itself. I cannot understand how to get the confidence interval [15+-5].

    What about the mean and the variance, I understood.

    Thank you in advance, I highly appreciate.
    All that is happening here is that your gamma distribution has a 95% interval [10,20] and you are modelling this with a symmetric normal 95% interval which has its mean at the centre of the interval and extends from (mean-1.96 sigma) to (mean + 1.96 sigma).

    CB
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