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In statistical mechanics, multiplicity (also called statistical weight) refers to the number of microstates corresponding to a particular macrostate of a thermodynamic system. [1] Commonly denoted , it is related to the configuration entropy of an isolated system [2] via Boltzmann's entropy formula where is the entropy and is the Boltzmann ...
In statistics, a weighted median of a sample is the 50% weighted percentile. [1][2][3] It was first proposed by F. Y. Edgeworth in 1888. [4][5] Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample.
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis ...
Weighted arithmetic mean. The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also ...
Probability density function. Box plot and probability density function of a normal distribution N(0, σ2). Geometric visualisation of the mode, median and mean of an arbitrary unimodal probability density function. [1] In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random ...
Unit-weighted regression is a method of robust regression that proceeds in three steps. First, predictors for the outcome of interest are selected; ideally, there should be good empirical or theoretical reasons for the selection. Second, the predictors are converted to a standard form. Finally, the predictors are added together, and this sum is ...
In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. Given a sample and weights , it is calculated as: [1] The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights ...
In chemistry, the mass fraction of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. [1] Expressed as a formula, the mass fraction is: tot {\displaystyle w_ {i}= {\frac {m_ {i}} {m_ {\text {tot}}}}.} Because the individual masses of the ingredients of a mixture sum ...