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In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample space. [1] Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event ...
Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics. New York: Charles Scribner's Sons . Sommerfeld, Arnold ; ed: F. Bopp, J. Meixner (1952).
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis.. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
The Jenks optimization method, also called the Jenks natural breaks classification method, is a data clustering method designed to determine the best arrangement of values into different classes. This is done by seeking to minimize each class's average deviation from the class mean, while maximizing each class's deviation from the means of the ...
Gibbs' book simplified statistical mechanics into a treatise of 207 pages. At the same time, Gibbs fully generalized and expanded statistical mechanics into the form in which it is known today. Gibbs showed how statistical mechanics could be used even to extend thermodynamics beyond classical thermodynamics, to systems of any number of degrees ...
In applied statistics, the Morris method for global sensitivity analysis is a so-called one-factor-at-a-time method, meaning that in each run only one input parameter is given a new value. It facilitates a global sensitivity analysis by making a number r {\displaystyle r} of local changes at different points x ( 1 → r ) {\displaystyle x(1 ...
The sign test is a statistical test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as ...
As for all statistical methods, a number of assumptions and approximations are inherently required for the application of ABC-based methods to real modeling problems. For example, setting the tolerance parameter ϵ {\displaystyle \epsilon } to zero ensures an exact result, but typically makes computations prohibitively expensive.