This paper addresses the challenge of point-supervised temporal action detection, in which only one frame per action instance is annotated in the training set. Self-training aims to provide supplementary supervision for the training process by generating pseudo-labels (action proposals) from a base model. However, most current methods generate action proposals by applying manually designed thresholds to action classification probabilities and treating adjacent snippets as independent entities. As a result, these methods struggle to generate complete action proposals, exhibit sensitivity to fluctuations in action classification scores, and generate redundant and overlapping action proposals. This paper proposes a novel framework termed ADM-Loc, which stands for Actionness Distribution Modeling for point-supervised action Localization. ADM-Loc generates action proposals by fitting a composite distribution, comprising both Gaussian and uniform distributions, to the action classification signals. This fitting process is tailored to each action class present in the video and is applied separately for each action instance, ensuring the distinctiveness of their distributions. ADM-Loc significantly enhances the alignment between the generated action proposals and ground-truth action instances and offers high-quality pseudo-labels for self-training. Moreover, to model action boundary snippets, it enforces consistency in action classification scores during training by employing Gaussian kernels, supervised with the proposed loss functions. ADM-Loc outperforms the state-of-the-art point-supervised methods on THUMOS14 and ActivityNet-v1.2 datasets.