# Generate random number from $P(x)=Ax^{-3/2}\exp(-B/x)$?

I wish to numerically generate a random number from the distribution $$P(x) = Ax^{-3/2}\exp(-B/x),\qquad A,B,x>0$$

What would be the easiest way of achieving this?

Inverse transform sampling does not seem appropriate since the above $P(x)$ does not have an analytical cumulative distribution function.

Rejection sampling requires a second distribution to draw samples from, but I don't know what known distribution would be efficient for this purpose.

If $X$ is distributed according to your density, then $\frac{2B}{X}$ has density proportional to $x^{-\tfrac{1}{2}} e^{-x/2}$. This is the density of a Chi-squared distribution with one degree of freedom, i.e. $X \stackrel{d}{=} \frac{2B}{N^2}$, where $N$ is a standard normal random variable.