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Recently, a suspicion arose that the free electrons in planetary nebulae (PNs) and H ii regions might have nonthermal energy distributions. In this scenario, a κ index is introduced to characterize the electron energy distributions, with smaller κ values indicating larger deviations from Maxwell–Boltzmann distributions. Assuming that this is the case, we determine the κ values for a sample of PNs and H ii regions by comparing the intensities of [O iii] collisionally excited lines and the hydrogen Balmer jump. We find the average κ indices of PNs and H ii regions to be 27 and 32, respectively. Correlations between the resultant κ values and various physical properties of the nebulae are examined to explore the potential origin of nonthermal electrons in photoionized gaseous nebulae. However, no positive result is obtained. Thus, the current analysis does not lend support to the idea that κ-distributed electrons are present in PNs and H ii regions. [ABSTRACT FROM AUTHOR]