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Normal and exponential-normal (?) distribution

by mahtabhossain
Tags: distribution, exponentialnormal, normal
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mahtabhossain
#1
Mar28-12, 12:30 AM
P: 2
Dear Users,

For normally distributed random variables x and y's p.d.f.:
[tex] \frac{1} {\sqrt{2\pi \sigma_x^2}}\exp\left\{- \frac{(x - \mu_x)^2}{2 \sigma_x^2}\right\} [/tex]
and
[tex] \frac{1} {\sqrt{2\pi \sigma_y^2}}\exp\left\{- \frac{(y - \mu_y)^2}{2 \sigma_y^2}\right\} [/tex]

What will be the p.d.f. of ln(x) - ln(y)? Is there any method to find it?

I think the followings are the p.d.f.s of u=ln(x) and v=ln(y) given x and y are normally distributed:
[tex] \frac{1} {\sqrt{2\pi \sigma_x^2}}\exp\left\{u - \frac{(e^u - \mu_x)^2}{2 \sigma_x^2}\right\} [/tex]
and
[tex] \frac{1} {\sqrt{2\pi \sigma_y^2}}\exp\left\{v - \frac{(e^v - \mu_y)^2}{2 \sigma_y^2}\right\} [/tex]

I am trying to find the p.d.f. of ln(x)-ln(y). Any suggestions?
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