Subtract two Log normal R.Vs

[sensor101]

Hello every one, here is the problem.
We have two Gaussian R.V's : z1 and z2 such that z1~N(mu1,sig1) and z2~N(mu2,sig2).

Now if have two other r.v's : x1 and x2 such that x1=exp(k.z1) and x2=exp(k.z2) where k

is some positive constant. Then clearly x1 and x2 are log normally distributed. I am

interested to find the distribution of x such that:

x=x1-x2 .

What is this new distribution which is the difference of two log normal distributions.

Many thanks in advance.

Sensor

[Dason]

Well using log rules it'll end up being the log of a Gaussian ratio distribution.

What do you want to do want to do with this exactly?

[sensor101]

Thanks for the response Dason.
I can't be taking the log of 'x', I need to know the distribution of 'x' as it is. However I can not find anything on the internet which discusses the subtraction of one lognormal rv from another.

thanks.

[Dason]

What exactly do you want to do with the distribution?

[sensor101]

Dason, I am working on analysis of two signals that are both log normally distributed. However, we extract data from them only if we subtract the signals (it linearises the system of equations ). I am trying to derive the Cramer Rao bound (CRB), for which i need the distribution of the difference of the two signals.

Thanks.