It is difficult to determine the distribution of wave periods even under the assumption that waves are linear and have narrow band frequency spectrum as they are often bimodal because sea states often have a certain percentage of cases with two wave systems. The existing wave period models due to their complexities are difficult for further mathematical treatments and hence their applications are limited to such as fitting to observed wave period distributions. In this study, the plausibility of finding the distribution of wave energy periods by modelling the empirical average conditional exceedances of energy periods are explored. Hence conditional mean functions (CMF) are derived from generalised Pareto, Erlang and three-parameter Weibull distributions. Since, CMF determines the distribution of energy periods uniquely, it is sufficient to find the functional form of CMF consistent with the data. This study utilises month wise clubbed every fifth day maximum significant wave heights (to mitigate serial dependency and to ensure sufficient sample size for analysis) and associated energy periods in winter (December to February) and extracted from 34 years SWAN generated data of a test site in the North Atlantic Ocean. The wave energy periods conditioned on significant wave heights < 4.0 m are considered since wave energy converters usually operate in shallow waters of depth < 4.0 m. The distribution of wave energy periods conditioned on significant wave heights is determined by modelling the empirically computed average conditional exceedance of wave energy periods with the CMF of generalised Pareto, Erlang and three-parameter Weibull distributions. Parametric relations are derived from Pareto and three parameter Weibull distributions to estimate certain energy period statistics of significance such as mean, mean maximum and most frequent maximum energy periods, average period of one-third the highest energy periods and the estimates are comparable with the empirical values. A general statistical formula is obtained based on order statistics to estimate the average period of one third the highest wave periods. A formula based on the general formula is derived from generalised Pareto distribution to estimate the average period of one-third the highest wave periods. There exists significant linear functional relationship between average period of one-third the highest wave heights computed from the data and average period of one-third the highest wave period estimates. The empirical ratio of significant wave period to mean wave period of 0.9-1.4 is well represented by the average energy period of one-third the highest significant wave heights to the mean energy period.