This paper introduces a non-Gaussian normative modelling approach using hierarchical Bayesian regression (HBR) with a flexible sinh-arcsinh (SHASH) distribution. The method extends traditional HBR to handle non-Gaussian data with heteroskedastic skewness and kurtosis, allowing for more accurate modelling of complex neuroimaging phenotypes. The SHASH distribution is used to model the data, with a reparameterisation that reduces parameter dependencies and improves sampling efficiency. The method is applied to a large multi-site neuroimaging dataset, demonstrating improved performance compared to a warped Bayesian linear regression baseline. The approach is particularly effective for highly nonlinear relationships between age and imaging-derived phenotypes, making it a valuable tool for normative modelling in precision psychiatry. The method is implemented in the open-source pcntoolkit and supports federated learning, enabling analysis of distributed datasets without data transportation. The paper also discusses the advantages and limitations of the approach, highlighting its potential to advance the field of normative modelling by better capturing uncertainty and variability in clinical data.This paper introduces a non-Gaussian normative modelling approach using hierarchical Bayesian regression (HBR) with a flexible sinh-arcsinh (SHASH) distribution. The method extends traditional HBR to handle non-Gaussian data with heteroskedastic skewness and kurtosis, allowing for more accurate modelling of complex neuroimaging phenotypes. The SHASH distribution is used to model the data, with a reparameterisation that reduces parameter dependencies and improves sampling efficiency. The method is applied to a large multi-site neuroimaging dataset, demonstrating improved performance compared to a warped Bayesian linear regression baseline. The approach is particularly effective for highly nonlinear relationships between age and imaging-derived phenotypes, making it a valuable tool for normative modelling in precision psychiatry. The method is implemented in the open-source pcntoolkit and supports federated learning, enabling analysis of distributed datasets without data transportation. The paper also discusses the advantages and limitations of the approach, highlighting its potential to advance the field of normative modelling by better capturing uncertainty and variability in clinical data.