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Method, computer program and apparatus for measuring a distribution of a physical variable in a region

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Moving average

In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, cumulative, or weighted forms (described below). A moving average filter is sometimes called a boxcar filter, especially when followed by decimation.

Logistic distribution

In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Moving-average model

In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable. Together with the autoregressive (AR) model, the moving-average model is a special case and key component of the more general ARMA and ARIMA models of time series, which have a more complicated stochastic structure.

Gumbel distribution

In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.

Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration.

First-past-the-post voting

First-past-the-post voting (FPTP or FPP) is an electoral system wherein voters cast a vote for a single candidate, and the candidate with the most votes wins the election. Analogous systems for multi-winner contests are known as plurality block voting or "block voting" systems; both FPTP and block voting are "plurality" systems in that the winner needs only a plurality (the greatest number) of the votes and not an absolute majority (greater than half).

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Heun's method

In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.

Two-round system

The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian result, not a simple-plurality result as under first past the post. Under the two-round election system, the election process usually proceeds to a second round only if in the first round no candidate received a simple majority (more than 50%) of votes cast, or some other lower prescribed percentage.