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

• Mar 20th 2013, 02:34 PM
ia88
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)?
• Mar 21st 2013, 04:19 AM
chiro
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