Intervalldata

Intervalldata is a data type used to represent values as intervals rather than precise points, capturing uncertainty or imprecision that arises from measurement error, rounding, or incomplete knowledge. It is commonly used in statistics, engineering, and data processing to reflect bounds on possible values.

A typical intervalldata item is a pair (low, high) with low ≤ high, representing the inclusive lower and upper limits of the value. Intervals may be closed or open on either end, and may carry metadata such as a confidence level or probability bounds to indicate the degree of certainty about the interval.

Operations on intervalldata include interval arithmetic, where the sum, difference, product, or quotient of intervals yields another interval that contains all possible results. Comparisons often rely on concepts like containment, overlap, or disjointness rather than exact ordering. Aggregation can use intersection, union, or center-radius representations to summarize multiple intervals.

Applications of intervalldata span measurement uncertainty and error propagation in science and engineering, data fusion from multiple sensors, robust statistics for censored or incomplete data, and risk assessment where bounds are preferred over point estimates. In databases and data processing, intervalldata can be stored as two numeric fields (lower and upper) or as a dedicated interval type, with performance considerations for queries that test overlaps or perform interval joins.

Related concepts include interval arithmetic, interval data analysis, and, more broadly, approaches to handling imprecise data such as fuzzy set theory. Intervalldata provides a practical framework for modeling and reasoning with bounded information.