I'm trying to understand the nature of limiting distributions and distributions, specifically
$1/Z_n \longrightarrow ~?$
where $Z_n\longrightarrow Z -Gaussian(0,1)$
I understand that the gamma distribution converges to the gaussian for a large enough $n$, so would it be inverted gamma until the $n$ is sufficiently large? But the wikipedia article for Inverted Gamma and Inverse Gaussian are completely different, even though they're both written as $IG( ~, ~)$
But I also have the same distribution as Inverted Gamma with $\alpha,\beta$ as parameters
Attempts: Let $Y=1/N$ where $N=Gaussian(0,1)$
$F(Y)=P(Y
But this gets me nothing that looks like what Wikipedia has