This paper introduces a new methodology for detecting anomalies in time\nseries data, with a primary application to monitoring the health of (micro-)\nservices and cloud resources. The main novelty in our approach is that instead\nof modeling time series consisting of real values or vectors of real values, we\nmodel time series of probability distributions over real values (or vectors).\nThis extension to time series of probability distributions allows the technique\nto be applied to the common scenario where the data is generated by requests\ncoming in to a service, which is then aggregated at a fixed temporal frequency.\nOur method is amenable to streaming anomaly detection and scales to monitoring\nfor anomalies on millions of time series. We show the superior accuracy of our\nmethod on synthetic and public real-world data. On the Yahoo Webscope data set,\nwe outperform the state of the art in 3 out of 4 data sets and we show that we\noutperform popular open-source anomaly detection tools by up to 17% average\nimprovement for a real-world data set.\n