Our work addresses the problem of egocentric human pose estimation from downwards-facing cameras on head-mounted devices (HMD). This presents a challenging scenario, as parts of the body often fall outside of the image or are occluded. Previous solutions minimize this problem by using fish-eye camera lenses to capture a wider view, but these can present hardware design issues. They also predict 2D heat-maps per joint and lift them to 3D space to deal with self-occlusions, but this requires large network architectures which are impractical to deploy on resource-constrained HMDs. We predict pose from images captured with conventional rectilinear camera lenses. This resolves hardware design issues, but means body parts are often out of frame. As such, we directly regress probabilistic joint rotations represented as matrix Fisher distributions for a parameterized body model. This allows us to quantify pose uncertainties and explain out-of-frame or occluded joints. This also removes the need to compute 2D heat-maps and allows for simplified DNN architectures which require less compute. Given the lack of egocentric datasets using rectilinear camera lenses, we introduce the SynthEgo dataset, a synthetic dataset with 60K stereo images containing high diversity of pose, shape, clothing and skin tone. Our approach achieves state-of-the-art results for this challenging configuration, reducing mean per-joint position error by 23% overall and 58% for the lower body. Our architecture also has eight times fewer parameters and runs twice as fast as the current state-of-the-art. Experiments show that training on our synthetic dataset leads to good generalization to real world images without fine-tuning.