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H is directly related to fractal dimension, D, and is a measure of a data series' "mild" or "wild" randomness. [4] The Hurst exponent is referred to as the "index of dependence" or "index of long-range dependence". It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction. [5]
This process is called raising the index. Raising and then lowering the same index (or conversely) are inverse operations, which is reflected in the metric and inverse metric tensors being inverse to each other (as is suggested by the terminology): = = =
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday non-mathematical or non-programming circumstances.
The rescaled range is a statistical measure of the variability of a time series introduced by the British hydrologist Harold Edwin Hurst (1880–1978). [1] Its purpose is to provide an assessment of how the apparent variability of a series changes with the length of the time-period being considered.
For instance, the 10% trimmed mean is the average of the 5th to 95th percentile of the data, while the 90% winsorized mean sets the bottom 5% to the 5th percentile, the top 5% to the 95th percentile, and then averages the data. Winsorizing thus does not change the total number of values in the data set, N.
Chronux – for neurobiological time series data; DAP – free replacement for SAS; Environment for DeveLoping KDD-Applications Supported by Index-Structures (ELKI) a software framework for developing data mining algorithms in Java; Epi Info – statistical software for epidemiology developed by Centers for Disease Control and Prevention (CDC).
The instantaneous rate of change is a well-defined concept that takes the ratio of the change in the dependent variable to the independent variable at a specific instant. This is an image of vials with different amounts of liquid. A continuous variable could be the volume of liquid in the vials. A discrete variable could be the number of vials.
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]