  A vexing puzzle in the study of planetary nebulae and \ion{H}{2} regions is
that the plasma diagnostic results based on collisionally excited lines
systematically differ from those based on recombination lines. A fairly
speculative interpretation is the presence of nonthermal electrons with the
so-called $\kappa$ energy distributions, yet there is little observational
evidence to verify or disprove this hypothesis. In this paper, we examine the
influence of $\kappa$-distributed electrons on the emissivities of \ion{O}{2}
recombination lines using an approximate method, where the rate coefficients
for a $\kappa$ distribution are computed by summing Maxwellian-Boltzmann rate
coefficients with appropriate weights. The results show that if invoking
$\kappa$-distributed electrons, the temperatures derived from the [\ion{O}{3}]
$(\lambda4959+\lambda5007)/\lambda4363$ ratios could coincide with those
estimated from the \ion{O}{2} $\lambda4649/\lambda4089$ ratios. However, the
estimated temperatures and $\kappa$ values are not in agreement with those
obtained through comparing the [\ion{O}{3}]
$(\lambda4959+\lambda5007)/\lambda4363$ ratios and the hydrogen recombination
spectra, suggesting that the electron energy is unlikely to follow the
$\kappa$-distributions over a global scale of the nebular regions.
Nevertheless, based on this observation alone, we cannot definitely rule out
the presence of $\kappa$-distributed electrons in some microstructures within
nebulae.
