mean and variance of reciprocal normal distribution

inverse probability-distributions normal-distribution

Mean and variance do not exist. For the mean to exist, the integral

$\int^\infty_{-\infty} e^{-\frac{(x-\mu)^2}{2\sigma^2}}\frac{1}{|x|} \text{d}x$

needs to be finite. This is clearly not the case.

Note it is necessary that mean exists for variance to exist.

See

http://en.wikipedia.org/wiki/Inverse_distribution#Reciprocal_normal_distribution

Note inverse gaussian is something completely different. It is connected to brownian motion hitting a level. I changed the title. The thing you are referring to is a reciprocal normal.

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