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Math Help - Support of a Distribution

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    Support of a Distribution

    Can someone define the term support of a distribution with a simple example? Thanks a lot.
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    Quote Originally Posted by vioravis View Post
    Can someone define the term support of a distribution with a simple example? Thanks a lot.
    Informally; it is the largets set on which the density (or mass function) is nowhere zero.

    RonL
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    Thanks, Captain. Is it possible for you to provide a mathematical example for this? I am particularly interested to know whether the density of two normal distributions with different supports can be multiplied and if so, what would be the resultant distribution.
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    Quote Originally Posted by vioravis View Post
    Thanks, Captain. Is it possible for you to provide a mathematical example for this? I am particularly interested to know whether the density of two normal distributions with different supports can be multiplied and if so, what would be the resultant distribution.
    What would having different supports mean in the context of the normal distribution, the support is the entire real line whatever the mean and standard deviation?

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    What would having different supports mean in the context of the normal distribution
    RonL
    Captain, that's what I am trying to understand myself. All I have is a methodology to sample from the product of two distributions (obtained from a professor) for a problem that I am working on and one of the necessary conditions to use this methodology is that the two distributions under consideration must have the same support. In most cases we would be considering Normal distributions for both and that's why I raised the question in the first place. Thanks.
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    Quote Originally Posted by vioravis View Post
    Captain, that's what I am trying to understand myself. All I have is a methodology to sample from the product of two distributions (obtained from a professor) for a problem that I am working on and one of the necessary conditions to use this methodology is that the two distributions under consideration must have the same support. In most cases we would be considering Normal distributions for both and that's why I raised the question in the first place. Thanks.
    Well if the methodology is for general distributions, but you have two normals you should not need to worry as they automaticaly have the same support.

    RonL
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    Captain,

    Do you mean to say that if we are considering different distributions the support would be different or otherwise it is always the same?

    I am still not able to understand the concept of support. A mathematical example would really help. Thanks a lot.
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    Quote Originally Posted by vioravis View Post
    Captain,

    Do you mean to say that if we are considering different distributions the support would be different or otherwise it is always the same?

    I am still not able to understand the concept of support. A mathematical example would really help. Thanks a lot.
    The method he gives may require that the distributions have the same support, but as you are using normals they do have the same support and so you don't have to worry.

    The uniform distribution on [0,1] has the interval [0,1] as its support, the exponetial distribution has support [0,\infty),

    The binomial distribution B(N,p) has support \{0, 1, .., N\}

    RonL
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    Captain,

    Thanks a lot. Is this true in case of multivariate normal also?
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    Quote Originally Posted by vioravis View Post
    Captain,

    Thanks a lot. Is this true in case of multivariate normal also?
    If you're familiar with the multivariate normal distribution you should suspect what the answer to this question is going to be .....
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    Fantastic,

    Thanks. But the answer is not too obvious to me. That is why I am asking. Has it got anything to do with the number of variables in each of the distributions?
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    Quote Originally Posted by vioravis View Post
    Fantastic,

    Thanks. But the answer is not too obvious to me. That is why I am asking. Has it got anything to do with the number of variables in each of the distributions?
    No. Two things:

    1. Recall the definition of support given by CaptainB.
    2. Look at the pdf for a multivariate normal.

    (The answer to the previous question is yes, the supports are the same in the multivariate normal case).
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    Fantastic,

    I understand that if the two multivariate normals have the same number of variables as in X1' = [X1, X2, X3] and X2' = [X1, X2, X3]. However, I am not able to see how it can extend to the following case:

    1. X1' = [X1, X2, X3] and X2' = [X1, X2, X3,X4] - There is an additional variable.

    Any help would be appreciated? Thanks a lot.
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    Quote Originally Posted by vioravis View Post
    Fantastic,

    I understand that if the two multivariate normals have the same number of variables as in X1' = [X1, X2, X3] and X2' = [X1, X2, X3]. However, I am not able to see how it can extend to the following case:

    1. X1' = [X1, X2, X3] and X2' = [X1, X2, X3,X4] - There is an additional variable.

    Any help would be appreciated? Thanks a lot.
    Sorry, I misunderstood. I think that you'd need the the dimensions to match. So I recant on my no. But ....... It's probably best to wait and see what CaptainB says as I'm not on solid ground here.
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    Thanks, fantastic. I will wait for Captain's answer.
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