Normal and exponential-normal (?) distribution

  1. 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]
    [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]
    [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?
  2. jcsd
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