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A (purely) periodic sequence (with period p), or a p-periodic sequence, is a sequence a 1, a 2, a 3, ... satisfying . a n+p = a n. for all values of n. [1] [2] [3] If a sequence is regarded as a function whose domain is the set of natural numbers, then a periodic sequence is simply a special type of periodic function.
A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive [2] constant P with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period.
The temporal mean is the arithmetic mean of a series of values over a time period. Assuming equidistant measuring or sampling times, it can be computed as the sum of the values over a period divided by the number of values. A simple moving average can be considered to be a sequence of temporal means over periods of equal duration.
A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, [1] landslides, [2] or river discharge flows to occur. It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let () be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every seconds, which is called the sampling interval or sampling period.
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values.. The DTFT is often used to analyze samples of a continuous function.
In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample ...