Power lawIn statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.
Gini coefficientIn economics, the Gini coefficient (ˈdʒiːni ), 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. The Gini coefficient measures the inequality among the values of a frequency distribution, such as levels of income.
Central limit theoremIn probability theory, the central limit theorem (CLT) establishes that, in many situations, for independent and identically distributed random variables, the sampling distribution of the standardized sample mean tends towards the standard normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.
Coefficient of variationIn probability theory and statistics, the coefficient of variation (COV), also known as Normalized Root-Mean-Square Deviation (NRMSD), Percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation to the mean (or its absolute value, , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
Fat-tailed distributionA fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed. Different research communities favor one or the other largely for historical reasons, and may have differences in the precise definition of either.
Conjugate priorIn Bayesian probability theory, if the posterior distribution is in the same probability distribution family as the prior probability distribution , the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function . A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution.
Multivariate normal distributionIn probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.
Long tailIn statistics and business, a long tail of some distributions of numbers is the portion of the distribution having many occurrences far from the "head" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc. The term is often used loosely, with no definition or an arbitrary definition, but precise definitions are possible. In statistics, the term long-tailed distribution has a narrow technical meaning, and is a subtype of heavy-tailed distribution.
ProbitIn probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and specialized regression modeling of binary response variables. Mathematically, the probit is the inverse of the cumulative distribution function of the standard normal distribution, which is denoted as , so the probit is defined as Largely because of the central limit theorem, the standard normal distribution plays a fundamental role in probability theory and statistics.
Geometric standard deviationIn probability theory and statistics, the geometric standard deviation (GSD) describes how spread out are a set of numbers whose preferred average is the geometric mean. For such data, it may be preferred to the more usual standard deviation. Note that unlike the usual arithmetic standard deviation, the geometric standard deviation is a multiplicative factor, and thus is dimensionless, rather than having the same dimension as the input values. Thus, the geometric standard deviation may be more appropriately called geometric SD factor.
Modern portfolio theoryModern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return.
