Dear colegues,
Good day
Suppose I have a random variable X∼Inverse Gamma(k,θ) , and I define:
Y=log(X)
I would like to find the probability density function of Y
Best wishes
Greetings, Huda,
As the log transformation is monotone, the density function can be derived with a simple Jacobian transformation. Taking y = log x, dy = dx/x = e-ydx, the transformed inverse gamma density is fY(y) = fX(ey) e–y = [θk / Γ(k)] exp(–k y – θ e-y).
With kind regards,
-Bryan
Greetings, Huda,
As the log transformation is monotone, the density function can be derived with a simple Jacobian transformation. Taking y = log x, dy = dx/x = e-ydx, the transformed inverse gamma density is fY(y) = fX(ey) e–y = [θk / Γ(k)] exp(–k y – θ e-y).
With kind regards,
-Bryan
Dear Dr Huda
The inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
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