  We investigate double $\Lambda$ hyperfragment formation from the statistical
decay of double $\Lambda$ compound nuclei produced in the $\Xi^-$ absorption at
rest in light nuclei, $^{12}\mathrm{C}$, $^{14}\mathrm{N}$ and
$^{16}\mathrm{O}$. We examine the target and the $\Lambda\Lambda$ bond energy
dependence of the double $\Lambda$ hyperfragment formation probabilities,
especially of those double hypernuclei observed in experiments. For the
$^{12}\mathrm{C}$ ($^{14}\mathrm{N}$) target, the formation probabilities of
$^{6}_{\Lambda\Lambda}\mathrm{He}$ and $^{10}_{\Lambda\Lambda}\mathrm{Be}$
($^{13}_{\Lambda\Lambda}\mathrm{B}$) are found to be reasonably large as they
are observed in the KEK-E373 (KEK-E176) experiment. By comparison, for
$^{16}\mathrm{O}$ target, the formation probability of
$^{11}_{\Lambda\Lambda}\mathrm{Be}$ is calculated to be small with $\Delta
B_{\Lambda\Lambda}$ consistent with the Nagara event. We also evaluate the
formation probability of ${}^{5}_{\Lambda\Lambda}\mathrm{H}$ from a
$\Xi^-$-${}^{6}\mathrm{He}$ bound state, ${}^{7}_{\Xi}\mathrm{H}$.
