  We consider the random transverse-field Ising model in $d=3$ dimensions with
long-range ferromagnetic interactions which decay as a power $\alpha > d$ with
the distance. Using a variant of the strong disorder renormalization group
method we study numerically the phase-transition point from the paramagnetic
side. The distribution of the (sample dependent) pseudo-critical points is
found to scale with $1/\ln L$, $L$ being the linear size of the sample.
Similarly, the critical magnetization scales with $(\ln L)^{\chi}/L^d$ and the
excitation energy behaves as $L^{-\alpha}$. Using extreme-value statistics we
argue that extrapolating from the ferromagnetic side the magnetization
approaches a finite limiting value and thus the transition is of mixed-order.
