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In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
Typically data is discretized into partitions of K equal lengths/width (equal intervals) or K% of the total data (equal frequencies). [1] Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method, [2] which uses mutual information to recursively define the best bins, CAIM, CACC, Ameva, and many others [3]
A pivot table is a table of values which are aggregations of groups of individual values from a more extensive table (such as from a database, spreadsheet, or business intelligence program) within one or more discrete categories. The aggregations or summaries of the groups of the individual terms might include sums, averages, counts, or other ...
Digital data can be contrasted with analog data, which is represented by a value from a continuous range of real numbers. Analog data is transmitted by an analog signal, which not only takes on continuous values but can vary continuously with time, a continuous real-valued function of time. An example is the air pressure variation in a sound wave.
Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal. When a discrete-time signal is obtained by sampling a sequence at uniformly spaced times, it has an associated sampling rate.
The concept of data type is similar to the concept of level of measurement, but more specific. For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale).
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equations [1] and are converse to discrete modelling. Modelling is generally broken down into several steps:
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .