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Math Help - Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

  1. #1
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    Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

    Hey folks!

    Are you able to provide a suitable reference (book, article, class notes, examples in R) to compute the

    P(|X|>x and |Y|>y)?


    Give thant X and Y ~BVN(mu1, mu2, sigma1, sigma2, rho) ?

    X and Y are actually standard normal variables with mean 0 and variance 1. The correlation is known, say, rho, and rho > 0.


    Sorry for my bad notation. My background in statistics is very limited.

    Thanks.

    Wallace
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  2. #2
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    Re: Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

    Hey DerWundermann.

    Just make the limits what they should be and partition them out.

    In one dimension you have Integral (a,b) f(x)dx + Integral (c,d) f(x)dx where a=-infinity,d=+infinity and a = -c gives P(|X| > a).

    You can apply the same idea except you are working on a two dimensional region instead of a one dimensional one.

    If there is no covariance between the two random variables then you will exclude a rectangle at the centre from your probability.

    If there is covariance structure, you will need to calculate your limits in a different way depending on the covariance.
    Thanks from DerWundermann
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    Re: Bivariate normal distribution - Conditional probability P(|X|>x and |Y|>y)

    Many thanks, Chiro!

    I will to digest your recommedation!
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