Two commonly used equations for this:
(GPM x PSI) / 1100 = HP
(GPM x PSI) / 1450 x 1.5 = HP
According to Russ, he prefers the second, giving the reason that the first pushes the engine to the limit constantly.
A GX390 is about 13 HP. So, lets say the bucket test confirms that it is putting out 5.5 GPM. Plug in the numbers, and solve for PSI:
5.5 x PSI / 1450 x 1.5 = 13
PSI = 2285
To compare with the first equation, it results in 2600.