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Math Help - Finding distr of ln(X) when know X binodal normal

  1. #1
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    Finding distr of ln(X) when know X binodal normal

    Hi.
    I am trying to find the distribution of ln(X) when i know that X is distributed as a binodal normal distribution, in other words:


    X \sim p \cdot N(a,\sigma^2) + (1-p) \cdot N(b,\sigma^2)
    which I suppose also can be written as  X \sim N( (p, 1-p) ( a, b)^T , \sigma^2).


    How do I then go about finding the distribution of ln(X)?
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  2. #2
    MHF Contributor
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    Re: Finding distr of ln(X) when know X binodal normal

    Hey la88.

    Take a look at the transformation theorem in probability:

    http://www2.econ.iastate.edu/classes...formations.pdf
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