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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.

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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.

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  • $\begingroup$ It works. Very neat solution, thanks. $\endgroup$ – lemon Dec 12 '16 at 12:34

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