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:

$\displaystyle X \sim p \cdot N(a,\sigma^2) + (1-p) \cdot N(b,\sigma^2) $

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

How do I then go about finding the distribution of ln(X)?

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