In economics, the Gini coefficient, also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality within a nation or a social group. It was developed by Italian statistician and sociologist Corrado Gini.
In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or .
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
The Herfindahl index is a measure of the size of firms in relation to the industry they are in and is an indicator of the amount of competition among them. Named after economists Orris C. Herfindahl and Albert O. Hirschman, it is an economic concept widely applied in competition law, antitrust regulation, and technology management. HHI has continued to be used by antitrust authorities, primarily to evaluate and understand how mergers will affect their associated markets. HHI is calculated by squaring the market share of each competing firm in the industry and then summing the resulting numbers. The result is proportional to the average market share, weighted by market share. As such, it can range from 0 to 1.0, moving from a huge number of very small firms to a single monopolistic producer. Increases in the HHI generally indicate a decrease in competition and an increase of market power, whereas decreases indicate the opposite. Alternatively, the index can be expressed per 10,000 "points". For example, an index of .25 is the same as 2,500 points.
In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a primary school to have a Pearson correlation coefficient significantly greater than 0, but less than 1.
In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function.
The unified neutral theory of biodiversity and biogeography is a theory and the title of a monograph by ecologist Stephen P. Hubbell. It aims to explain the diversity and relative abundance of species in ecological communities. Like other neutral theories of ecology, Hubbell assumes that the differences between members of an ecological community of trophically similar species are "neutral", or irrelevant to their success. This implies that niche differences do not influence abundance and the abundance of each species follows a random walk. The theory has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.
The Jaccard index is a statistic used for gauging the similarity and diversity of sample sets. It is defined in general taking the ratio of two sizes, the intersection size divided by the union size, also called intersection over union (IoU).
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable and finds a linear function that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor.
Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree of differentiation. Populations with many similar alleles have small genetic distances. This indicates that they are closely related and have a recent common ancestor.
A diversity index is a method of measuring how many different types there are in a dataset. Some more sophisticated indices also account for the phylogenetic relatedness among the types. Diversity indices are statistical representations of different aspects of biodiversity, which are useful simplifications for comparing different communities or sites.
The Rand index or Rand measure in statistics, and in particular in data clustering, is a measure of the similarity between two data clusterings. A form of the Rand index may be defined that is adjusted for the chance grouping of elements, this is the adjusted Rand index. The Rand index is the accuracy of determining if a link belongs within a cluster or not.
The mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn from a probability distribution. A related statistic is the relative mean absolute difference, which is the mean absolute difference divided by the arithmetic mean, and equal to twice the Gini coefficient. The mean absolute difference is also known as the absolute mean difference and the Gini mean difference (GMD). The mean absolute difference is sometimes denoted by Δ or as MD.
In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. When determining the numerical relationship between two variables of interest, using their correlation coefficient will give misleading results if there is another confounding variable that is numerically related to both variables of interest. This misleading information can be avoided by controlling for the confounding variable, which is done by computing the partial correlation coefficient. This is precisely the motivation for including other right-side variables in a multiple regression; but while multiple regression gives unbiased results for the effect size, it does not give a numerical value of a measure of the strength of the relationship between the two variables of interest.
An index of qualitative variation (IQV) is a measure of statistical dispersion in nominal distributions. Examples include the variation ratio or the information entropy.
The Dice-Sørensen coefficient is a statistic used to gauge the similarity of two samples. It was independently developed by the botanists Lee Raymond Dice and Thorvald Sørensen, who published in 1945 and 1948 respectively.
In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.
In ecology and biology, the Bray–Curtis dissimilarity is a statistic used to quantify the dissimilarity in species composition between two different sites, based on counts at each site. It is named after J. Roger Bray and John T. Curtis who first presented it in a paper in 1957.
Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship. It is named after the ecologist who first proposed it in 1961, Lionel Roy Taylor (1924–2007). Taylor's original name for this relationship was the law of the mean. The name Taylor's law was coined by Southwood in 1966.
