We predict the conditional distributions of service metrics, such as response time or frame rate, from infrastructure measurements in a networked environment. From such distributions, key statistics of the service metrics, including mean, variance, or quantiles can be computed, which are essential for predicting SLA conformance and enabling service assurance. We present and assess two methods for prediction: (3) mixture models with Gaussian or Lognormal kernels, whose parameters are estimated using mixture density networks, a class of neural networks, and (4) histogram models, which require the target space to be discretized. We apply these methods to a VoD service and a KV store service running on our lab testbed. A comparative evaluation shows the relative effectiveness of the methods when applied to operational data. We find that both methods allow for accurate prediction. While mixture models provide a general and elegant solution, they incur a very high overhead related to hyper-parameter search and neural network training. Histogram models, on the other hand, allow for efficient training, but require adjustment to the specific use case.