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The minor planets on orbits that are dynamically stable in Neptune's 1:1 resonance on Gyr timescales were likely em:laced by Neptune's outward migration. We explore the intrinsic libration amplitude, eccentricity, and inclination distribution of Neptune's stable Trojans, using the detections and survey efficiency of the Outer Solar System Origins Survey (OSSOS) and Pan-STARRS1. We find that the libration amplitude of the stable Neptunian Trojan population can be well modeled as a Rayleigh distribution with a libration amplitude width σ A ϕ of 15°. When taken as a whole, the Neptune Trojan population can be acceptably modeled with a Rayleigh eccentricity distribution of width σ e of 0.045 and a typical sin(i) × Gaussian inclination distribution with a width σ i of 14 ± 2 ∘ ; however, these distributions are only marginally acceptable. This is likely because, even after accounting for survey detection biases, the known large (H r < 8) and small (H r ≥ 8) Neptune Trojans appear to have markedly different eccentricities and inclinations. We propose that like the classical Kuiper belt, the stable intrinsic Neptunian Trojan population have dynamically 'hot' and dynamically 'cold' components to its eccentricity/inclination distribution, with σ e − c o l d ∼ 0. 02 / σ i − c o l d ∼ 6 ° and σ e − h o t ∼ 0. 05 / σ i − h o t ∼ 18 °. In this scenario, the 'cold' L4 Neptunian Trojan population lacks the H r ≥ 8. 0 members and has 1 3 − 6 + 11 'cold' Trojans with H r < 8. 0. On the other hand, the 'hot' L4 Neptunian Trojan population has 13 6 − 75 + 84 Trojans with H r < 10 — a population 2.4 times greater than that of the L4 Jovian Trojans in the same luminosity range. • The orbital distribution and total population of Neptune's stable L4 Trojans have been studied. • The libration amplitude can be modeled as a Rayleigh distribution with a libration amplitude width of 15 degrees. • The eccentricity/inclination distribution is more difficult to be modeled by a single Rayleigh distribution. • We presented two components population model, which has a low eccentricity/inclination 'cold' and a high eccentricity/inclination 'hot' components on L4 Neptunian Trojan population to model the observation result. [ABSTRACT FROM AUTHOR]