PDF attributes

Orion 2.0 supports both continuous and discrete uncertainty, which are represented using their pdfs. This has been illustrated in our sensor data example in Table 1 (continuous uncertainty) and Table 2 (discrete uncertainty). The uncertainty in many applications can be expressed using standard distributions. Orion has built-in support for commonly used continuous (e.g. Gaussian, Uniform) and discrete (e.g. Binomial, Poisson) distributions. These uncertain values are processed symbolically in the database. For example, when the Gaussian distribution is used, we only store the mean and variance as the two parameters of the distribution, as shown in Table 1. When the underlying data cannot be represented using standard distributions, Orion automatically converts them to approximate distributions, including histograms and discrete sampling. The histogram distribution consists of buckets over the data domain, along with the probability density in each bucket. The discrete sampling simply consists of multiple value probability pairs. The bin size (or number of sampling points) is an important parameter that decides the trade-off between accuracy and efficiency.