Mellin transform

Mellin transform (plural Mellin transforms)

Mellin transforms (plural)
Mellin-transform (alternative)

Named after Finnish mathematician Hjalmar Mellin.

This chapter is concerned with the theory and applications of the Mellin transform. We derive the Mellin transform and its inverse from the complex Fourier transform. This is followed by several examples and the basic operational properties of Mellin transforms.

1995, Lokenath Debnath, Integral Transforms and Their Applications, CRC Press, page 211:

2005, Robb J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley & Sons, page 303,
If X is a positive random variable with density function f(x), the Mellin transform M(s) gives the (s-l)th moment of X. Hence Theorem 8.2.6 gives the Mellin transform of W evaluated at s=h+1; that is,
M(h+1)=E(Wʰ).
The inverse Mellin transform gives the density function of W.

In Chapters 2 and 7, the Mellin transform of the exponential function and the inverse Mellin transform of the Gamma function play key roles in demonstrating the equivalence of the modular relation and the functional equation. In proving the identities in this chapter, Mellin transforms also play central roles.

2008, Bruce C. Berndt, Marvin I. Knopp, Hecke's Theory of Modular Forms and Dirichlet Series, World Scientific, page 115:

mathematical analysis
mathematical analysis

(mathematical analysis, number theory, statistics) An integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform.


multideviation

(statistics) A distance of more than two standard deviations from the mean.


negative binomial distribution

en-noun

negative binomial distribution (plural negative binomial distributions)

negative binomial distributions (plural)

(statistics) A discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.


Yule-Simon distribution

Named after Udny Yule and Herbert A. Simon. Simon originally called it the Yule distribution.

(statistics) A certain discrete probability distribution.


bipower

In this paper we study the effects of noise on the bipower variation (BPV), realized volatility (RV) and testing for co-jumps in high-frequency data under the small noise framework.

2016, Daisuke Kurisu, “Power variations and testing for co-jumps: the small noise approach”, in arXiv:

(statistics) An alternative to variance; a measure of variability based on summing the product of adjacent data points rather than summing the squares of data points.


alpha level

(statistics) The significance level of a statistical test.


Rademacher distribution

probability distribution
probability distribution

(probability theory, statistics) A discrete probability distribution where a random variate has a 50% chance of being +1 and a 50% chance of being -1.


outlyingness

(statistics, of a data point, etc.) The measure, degree or quality of being an outlier.


MSE

MSE (countable and uncountable, plural MSEs)

(statistics) Initialism of mean squared error.


MSD

MSD (countable and uncountable, plural MSDs)

mean squared deviation
w:mean squared deviation

(statistics) Initialism of mean squared deviation.

mean squared displacement
w:mean squared displacement

(statistics) Initialism of mean squared displacement.


compressed sensing

(statistics, signal processing) A signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.


centerpoint

LL-Q1860 (eng)-Flame, not lame-centerpoint.wav

(statistics, geometry) A generalization of the median to data in higher-dimensional Euclidean space.


CFA

confirmatory factor analysis
w:confirmatory factor analysis

(statistics) Initialism of confirmatory factor analysis.


Rice distribution

Rice distribution (plural Rice distributions)

Rice distributions (plural)
Ricean distribution (alternative)
Rician distribution (alternative)

(statistics) The probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean.


trimean

(statistics) A measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles.


studentization

From student (“pseuodnym of William Sealy Gossett”) + -ization.

suffix

(statistics, originally) The use of Student's t-test.

(statistics, generally) The determination or use of a sampling distribution that is independent of nuisance parameters of the population distribution, which are not directly relevant to the estimates or tests of significance of primary interest.


nuisance parameter

en-noun

nuisance parameter (plural nuisance parameters)

For instance, applications require to specify the number of hidden layers [of a neural network], the number of neurons, the form of the activation function, the algorithm, as well as associated nuisance parameters used for training the models.

2025, Niko Hauzenberger, Florian Huber, Karin Klieber, Massimiliano Marcellino, “Bayesian neural networks for macroeconomic analysis”, in Journal of Econometrics, number 249:

(statistics) A parameter of the distribution of a population that is not directly relevant to solving the significance test or estimate problem under consideration.


Wishart distribution

Wishart distribution (plural Wishart distributions)

Named in honour of Scottish mathematician John Wishart, who formulated the distribution in 1928.

The novelty of this work lies in its incorporation of a general conjugate prior distribution for the covariance matrix, namely a generalized inverted Wishart distribution (GIW). As its name suggests, this distribution, discovered by Brown et al. (1994b) generalizes the well-known inverted Wishart distribution.

2006, Nhu D. Le, James V. Zidek, Statistical Analysis of Environmental Space-Time Processes, Springer, page 142:

The basic properties of Wishart distributions are studied in Section 7.3.

2008, Martin Bilodeau, David Brenner, Theory of Multivariate Statistics, Springer, page 85:

Recall from Appendix B that the Wishart distribution W#95;d(#92;Sigma,n) is characterized by a positive definite matrix #92;Sigma and the degrees of freedom n.

2015, Sudharman K. Jayaweera, Signal Processing for Cognitive Radios, Wiley, page 459:

chi-square distribution
chi-square distribution

(statistics) A generalisation of the chi-square distribution to an arbitrary (integer) number of dimensions, or of the gamma distribution to a non-integer number of degrees of freedom.


sample path

sample paths (plural)
sample-path (alternative)

1968, Leo Breiman, Probability, 1992, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 298,
These processes cannot have versions with continuous sample paths, otherwise the argument given in Chapter 12 forces them to be Brownian motion.

1981 [Wiley], Robert J. Adler, The Geometry of Random Fields, 2010, Society for Industrial and Applied Mathematics, Unabridged republication, page 39,
In order to study the 'finite' situation it is necessary to impose a number of conditions on the sample paths of the fields. Indeed, what we shall later generally assume is that sample paths belong, with probability one, to the special class of functions we now define.

A sample path or stochastic realization of the stochastic process #92;#123;#92;mathcal#123;I#125;(t)#92;#125;#92;infty#95;#123;t#61;0#125; for t#92;in#92;#123;0,#92;Deltat,2#92;Deltat,...#92;#125; is an assignment of a possible value to #92;mathcal#123;I#125;(t) based on the probability vector p(t).[…]Three sample paths of the stochastic model are compared to the deterministic solution in Fig.3.4. One of the sample paths is absorbed before 200 time steps (the population following this path becomes disease-free) but two sample paths are not absorbed during 2,000 time steps.

2008, Linda J. S. Allen, “Chapter 3: An Introduction to Stochastic Epidemic Models”, in Fred Brauer, Pauline van den Driessche, Jianhong Wu, editors, Mathematical Epidemiology, Springer, page 90:

(statistics) Any set of possible values to which the appropriate random variables determined by a stochastic process might map a given point in the sample space, taken over all values of the index space (often regarded as time).

stochastic realisation

set of values for a given point of sample space


normal random variable

normal random variable (plural normal random variables)

Since this density function cannot be integrated directly, in order to find probabilities involving normal random variables, we must resort to tables giving us various percentile points of the distribution.

1986, Mark C. K. Yang, David H. Robinson, Understanding and Learning Statistics by Computer, World Scientific, page 28:

Although normal random variables are continuous, they are often used to model discrete quantities.[…]The probability density function of a normal random variable depends on two parameters, denoted μ and σ, which are, respectively, the mean and standard deviation of the random variable.

2016, Geoffrey C. Berresford, Andrew M. Rockett, Applied Calculus, 7th edition, Cengage Learning, page 731:

A special type of continuous random variable, known as a normal random variable, is studied.[…]We present the additive property of normal random variables. The percentiles of normal random variables are studied.

2017, Sheldon M. Ross, Introductory Statistics, 4th edition, Elsevier (Academic Press), page 263:

(probability theory, statistics) A random variable whose probability distribution is a normal distribution.


cross-countries

diminishing cross-countries disparities in Internet use

(statistics, of comparative data) Across or between countries.


standard normal random variable

standard normal random variable (plural standard normal random variables)

standard normal random variables (plural)

Suppose X#92;simN(#92;mu,#92;sigma). Then
Z#61;#92;frac#123;x-#92;mu#125;#123;#92;sigma#125;
is a standard normal random variable. In other words, any normal random variable can be standardized by subtracting the mean from the variable and dividing the difference by the standard deviation.

2000, George E. Monahan, Management Decision Making: Spreadsheet modeling, analysis, and applications, volume 1, Cambridge University Press, page 405:

This technique is based on a polynomial transformation that proceeds by taking the sum of a linear combination of a standard normal random variable, its square, and its cube.

2010, Todd C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations, Taylor & Francis (CRC Press), page 1:

2016, Maria Dolores Ugarte, Ana F. Militino, Alan T. Arnholt, Probability and Statistics with R, 2nd Edition, Taylor & Francis (CRC Press), page 297,
A normal random variable with μ = 0 and σ = 1, often denoted Z, is called a standard normal random variable. […] Further, any normal random variable can be converted to a standard normal random variable using (4.25).

standard normal distribution
standard normal distribution

(probability theory, statistics) A random variable whose probability distribution is a standard normal distribution.


percentilation

(statistics) The division of a distribution into percentiles


hypergeometric random variable

hypergeometric random variable (plural hypergeometric random variables)

hypergeometric random variables (plural)

Computer generation of classical hypergeometric random variables has been discussed in detail by Kachitvichyanukul and Schmeiser (1985).

1992, Norman Lloyd Johnson, Samuel Kotz, Adrienne W. Kemp, Univariate Discrete Distributions, page 67:

Chapter 6 introduces testing of hypotheses immediately after the study of binomial and hypergeometric random variables.

2005, Martin Buntinas, Gerald Marlowe Funk, Statistics for the Sciences, page xv:

If #92;textstyleX is a hypergeometric random variable, then the variance is #92;textstyleVar(X)#61;#92;left(#92;frac#123;M#125;#123;N#125;#92;right)n#92;left(1-#92;frac#123;M#125;#123;N#125;#92;right)#92;left(1-#92;frac#123;n-1#125;#123;N-1#125;#92;right).

2007, Purna Chandra Biswal, Probability and Statistics, India: Prentice-Hall, published 2008, page 87:

Thus, whereas the expected value of the hypergeometric random variable with parameters n, N, p is the same as that of the binomial random variable with parameters n, p, its variance is smaller than that of the binomial by the factor (N − n)/(N − 1).

2017, Sheldon M. Ross, Introductory Statistics, Elsevier (Academic Press), page 250:

hypergeometric distribution
hypergeometric distribution

(probability theory, statistics) A random variable whose probability distribution is a hypergeometric distribution.

хипергеометрична случайна величина

random variable with hypergeometric distribution


millile

(statistics) Any of the values in a series that divides the distribution of individuals in that series into a thousand groups of equal frequency.


quadratic form

Quadratic form
Quadratic form (statistics)

Quadratic forms of normal random vectors are of great importance in many branches of statistics, such as least-squares methods, the analysis of variance, regression analysis, and experimental design.

2009, Allan Gut, An Intermediate Course in Probability, 2nd edition, Springer, page 136:

(statistics, multivariate statistics) A scalar quantity of the form εᵀΛε, where ε is a vector of n random variables, and Λ is an n-dimensional symmetric matrix.


beta distribution

beta distribution (plural beta distributions)

In particular, I illustrate how a hierarchical model in which the allele frequency distribution among populations is approximated by a Beta distribution and distribution of mean allele frequencies across loci is also approximated by a Beta distribution, accounts for the time-correlation of allele frequencies that existing methods of inference ignore.

2006, Kent E. Holsinger, “Chapter 2: Bayesian hierarchical models in geographical genetics”, in James S. Clark, Alan E. Gelfand, editors, Hierarchical Modelling for the Environmental Sciences: Statistical Methods and Applications, Oxford University Press, page 25:

2014, Stephen F. Bush, Smart Grid: Communication-Enabled Intelligence for the Electric Power Grid, Wiley, 2015, Reprint with corrections, page 366,
When more than two mutually exclusive events are involved in a frame of reference, the beta distributions form the marginals of a Dirichlet distribution.

2014, Nikolay Tcholtchev, Ina Schieferdecker, Framework for Ensuring Runtime Stability of Control Loops in Multi-agent Networked Environments, Marina Gavrilova, C. J. Kenneth Tan (editors), Transactions on Computational Science XXII, Springer, LNCS 8360, page 80,
We developed a Matlab script that implements the machine learning procedures as specified by (11), as well as by (13) with applying the beta-distribution (14) as a probability measure.

(probability, statistics) Any of a family of continuous probability distributions defined on the interval [0, 1] whose shape is parametrised by two positive parameters, denoted α and β, which appear as exponents in the associated random variable.


KAP

KAP (countable and uncountable, plural KAPs)

(statistics) Initialism of knowledge, attitude(s), and practice(s): a type of representative survey, originated in the 1950s, that examines the level of knowledge, beliefs, and behaviours of a population in the context of a specific topic.


agrimetric

Under Ambassador's direction and in light new aid concepts, team will undertake such exploration and will review US assistance to Thailand, including specifically such items as […] (e) community development, including agrimetric centers in border areas, particularly Northeast.

1994, “Thailand”, in Foreign Relations of the United States, 1961–1963: Southeast Asia, volume XXIII, Washington: United States Department of State: United States Government Printing Office, →ISBN, page 878:

Data and technology have a central role to play in increasing the productivity and competitiveness of British farming. Last October, I launched the first of our agri-tech centres of excellence, the agrimetric centre at Rothamsted. They will develop new software models to improve our ability to understand and utilise the huge volume of data that exist.

2016 May 5, The Minister of State, Department for Environment, Food and Rural Affairs (George Eustice), “Commons Chamber: Oral Answers to Questions: Department for Environment, Food and Rural Affairs: British Farming”, in House of Commons Hansard (House of Commons), volume 609, column 293:

(statistics, agriculture) Relating to agrimetrics.


agrimetrics

We're South Africa's science councils Agricultural Research Council— Made up of 13 institutes covering topics from agrimetrics and plant biotechnology, to research on crops, soil and pests.

1994, New Scientist, volume 141, numbers 1908-1918, page 13:

For the third straight year Hybrid Turkeys leads in both independent strain studies and agrimetrics summaries.

1997, International Hatchery Practice, volumes 12-13:

Quantifiable comparisons are done sequentially, examining: • within peer group comparisons, such as agrimetrics; • within system farm-level mean measures; • within system measures of variance; and • within production flow measures using descriptive measures.

2003, David E. Reeves, “Benchmarking reproductive performance within production systems”, in 2003 Allen D. Leman Swine Conference:

• Mapping and enhancing different decision making tools for farmers • Influencing EC to develop agrimetrics data • Adopting and developing emerging technologies and infrastructures

2016, Report of the kick off meeting of the Knowledge Network on Sustainable Intensification (KNSI), 3 June 2016, Wageningen:

(statistics, agriculture) The measurement of fields or agricultural data.


Fleiss' kappa

(statistics) A statistical measure for assessing the reliability of agreement between a fixed number of raters.


Sobel test

Based on the work of Michael E. Sobel, a statistics professor at Columbia University, New York.

(statistics) A kind of specialized t test that tests the significance of a mediation effect.


ARMA

(statistics) Initialism of autoregressive moving average


ARIMA

(statistics) Initialism of autoregressive integrated moving average.


ARCH

(statistics) Initialism of autoregressive conditional heteroskedasticity


GARCH

(statistics) Initialism of generalised autoregressive conditional heteroskedasticity


arithmetic average

arithmetic average (plural arithmetic averages)


Wilson score interval

Wilson score interval (plural Wilson score intervals)

Developed by Edwin Bidwell Wilson (1927).

(statistics) An improvement over the normal binomial approximation interval in that the actual coverage probability is closer to the nominal value.


residual sum of squares

residual sum of squares (plural residual sums of squares)

(statistics) The sum of the squared residuals between some model and a data set; a measure of how well the model fits with the data.


relative frequency

relative frequency (plural relative frequencies)

(statistics) The number of data points satisfying something divided by the total number of data points.


absolute frequency

absolute frequency (plural absolute frequencies)

(statistics) the number of data points satisfying something


downweight

en-verb

downweight (third-person singular simple present downweights, present participle downweighting, simple past and past participle downweighted)

downweights (present singular third-person)
downweighting (participle present)
downweighted (participle past)
downweighted (past)

(statistics) To give something a lower weight


bincount

(statistics) A count of the number of things in each element of an array


binsize

(statistics) The number of things in each element of an array


undercoverage

LL-Q1860 (eng)-Flame, not lame-undercoverage.wav

(statistics) Insufficient coverage (inadequate representation in a sample)


studentize

studentize (third-person singular simple present studentizes, present participle studentizing, simple past and past participle studentized)

studentizes (present singular third-person)
studentizing (participle present)
studentized (participle past)
studentized (past)

(statistics, transitive) To perform studentization on.


projection matrix

en-noun

projection matrix (plural projection matrices)

Caswell (1989) pointed out that most linear stage-structured models have both primitive and irreducible projection matrices.[…]The projection matrix M shown in the table is then calculated as PS + R.

1999, Terrance J. Quinn II, Richard B. Deriso, Quantitative Fish Dynamics, Oxford University Press, page 372:

We then turn to applications of population projection matrices both for natural resource management and for conservation.

2013, John H. Vandermeer, Deborah E. Goldberg, Population Ecology: First Principles, 2nd edition, Princeton University Press, page 62:

(statistics) A matrix that maps a vector of response (dependent variable) values to a vector of fitted or predicted values.


sequantitative

An initial sequantitative determination of EPM—1 in 20 sera of healthy donors and 28 patients with gastrointestinal tumors revealed that all sera of healthy donors contain high levels, in contrast to the majority of tumor sera (20/28) which had low or no detectable levels.

1987, Gastroenterology - Volume 92, page 1371:

The favorable reliability and objectiveness of this evaluation system appear to be due to partly, at least, introducing a sequantitative mycological assessment criterion.

2000, Kenji Nagino, Hiroshi Shimohira, Masatoshi Ogawa, Katsuhisa Uchida, Hideyo Yamaguchi, “Comparison of the therapeutic efficacy of oral doses of fluconazole and griseofulvin in a guinea pig model of dermatophytosis”, in The Journal of Antibiotics, volume 53, number 2:

Figure 1 Confirmation of microarray results by sequantitative RT-PCR analysis.

2005 January, Sophie Vasseur, Cédric Malicet, Ezequiel L Calvo, Jean Charles Dagorn, Juan L Iovanna, “Gene expression profiling of tumours derived from rasⱽ¹²/E1A-transformed mouse embryonic fibroblasts to identify genes required for tumour development”, in Molecular Cancer, volume 4, number 4:

(statistics) Pertaining to the quantitative analysis of autocorrelation in sequence data.


probable error

probable error (countable and uncountable, plural probable errors)

(statistics) The half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside.


regulize

en-verb

regulize (third-person singular simple present regulizes, present participle regulizing, simple past and past participle regulized)

regulizes (present singular third-person)
regulizing (participle present)
regulized (participle past)
regulized (past)

From Latin regulare (“to direct, rule, regulate”), from regula (“rule”), from regere (“to keep straight, direct, govern, rule”) + -ize.

der

Let p be the threshold wherefrom output signal begins to appear and P the saturation threshold, beyond which the output signal values remain constant. We regulize this interval by considering it is equal to the unity.

1988, Academia de Studii Economice (Romania), Economic Computation and Economic Cybernetics Studies and Research:

The development of the boundary integral equations exploits (as usual) Somigliana's identity but a special manipulation is carried out to "regulize" certain integrals associated with the crack line.

1996, Applied Mechanics Reviews - Volume 49, Issues 7-9, page 40:

We regulize by dropout (p = 0.25) just before the fully connected layer.

2018, Danail Stoyanov, Understanding and Interpreting Machine Learning in Medical Image Computing Applications, →ISBN:

(statistics) To manipulate data so that it is on a comparable scale; normalize.


binwidth

(statistics) The numerical width of a bin


presmooth

en-verb

presmooth (third-person singular simple present presmooths, present participle presmoothing, simple past and past participle presmoothed)

presmooths (present singular third-person)
presmoothing (participle present)
presmoothed (participle past)
presmoothed (past)

to presmooth a distribution

(transitive, statistics) To smooth in advance.


equiquantal

(statistics) Relating to equal quantities


hyperdistribution

en-noun

hyperdistribution (countable and uncountable, plural hyperdistributions)

The simplest approach to estimating hyperdistribution is to plot the frequency distribution of parameter estimates available for all stocks of interest.

1998, National Research Council, Division on Earth and Life Studies, Ocean Studies Board, Improving Fish Stock Assessments, →ISBN, page 34:

Prior distributions for the hyperdistribution parameters are considered to be relatively uninformative distributions.

2008, David L. Thomson, Evan G. Cooch, Michael J. Conroy, Modeling Demographic Processes in Marked Populations, →ISBN, page 1126:

In superstatistics, the hyperdistribution f(η) is determined by the physical problem that one wants to model.

2011, Jan Naudts, Generalised Thermostatistics, →ISBN, page 74:

(statistics, countable) A parameterized set of probability distributions.


TOI

TOI (countable and uncountable, plural TOIs)

(ice hockey statistics) Icetime; Abbreviation of time on ice.


geoadditive

(statistics, of a model) Obtained by the addition of multiple geographically separate models


sigmoid function

sigmoid function (plural sigmoid functions)

1995, Jun Han, Claudio Moraga, The Influence of the Sigmoid Function Parameters on the Speed of Backpropagation Learning, José Mira, Francisco Sandoval (editors), From Natural to Artificial Neural Computation: International Workshop on Artificial Neural Networks, Proceedings, Springer, LNCS 930, page 195,
[The] [s]igmoid function is the most commonly known function used in feed forward neural networks because of its nonlinearity and the computational simplicity of its derivative.

The first significant new insight from gamma spatial analysis emerged on re-examination of the sigmoid function representing bilateral saturation.

2012, Walter Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Springer, page 241:

2016, Roumen Anguelov, Svetoslav Markov, Hausdorff Continuous Interval Functions and Applications, Marco Nehmeier, Jürgen Wolff von Gudenberg, Warwick Tucker (editors), Scientific Computing, Computer Arithmetic, and Validated Numerics: 16th International Symposium, SCAN 2014, Springer, LNCS 9553, page 10,
Sigmoid functions find multiple applications to neural networks and cell growth population models [14,20]. A sigmoid function on R with a range [a,b] is defined as a monotone function s(t): R →[a,b] such that lim _(t→-∞)s(t)=a, and lim _(t→∞)s(t)=b.

(mathematical analysis, statistics) Any of various real functions whose graph resembles an elongated letter "S"; specifically, the logistic function y=(eˣ)/(eˣ+1)=1/(1+e⁻ˣ).


pseudoresidual

LL-Q1860 (eng)-Flame, not lame-pseudoresidual.wav

(statistics) The difference between the observed value and the median


Sørensen-Dice coefficient

Sørensen–Dice coefficient (plural Sørensen-Dice coefficients)

Sørensen–Dice coefficient (canonical)
Sørensen-Dice coefficients (plural)

Developed independently by the botanists Thorvald Sørensen and Lee Raymond Dice in the 1940s.

(statistics) A statistic used to gauge the similarity of two samples. It is equal to twice the number of elements common to both sets, divided by the sum of the number of elements in each set.


Jaccard index

Jaccard index (plural Jaccard indexes or Jaccard indices)

Jaccard indexes (plural)
Jaccard indices (plural)

Developed by Swiss botanist Paul Jaccard (1868–1944), who gave it the French name coefficient de communauté.

(statistics) A statistic for gauging the similarity and diversity of sample sets, based on the size of the intersection between the sets divided by the size of the union of the sets.


disattenuation

disattenuation (usually uncountable, plural disattenuations)

(statistics) A correction to account for attenuation


Wald test

(statistics) A test that assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate.


Fisher information

Named after the statistician Ronald Fisher.

(statistics) A measure of the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.


overfactorization

Shall we stop the process of factoring at this point, or go on to test a third hypothesis? […] The question of when to stop factoring is one of the major points of controversy in factor analysis, and the criticisms which one factorist may direct against the work of another quite commonly deal with charges of overfactorization and underfactorization.

1959, Solomon Diamond, Information and error, pages 224–225:

(statistics) The use or consideration of excessive factors in factor analysis.


Chapman-Robbins bound

Chapman-Robbins bound (plural Chapman-Robbins bounds)

Named after Douglas Chapman and Herbert Robbins, who discovered it in 1951, independently of the original (1950) discovery by John Hammersley.

(statistics) A lower bound on the variance of estimators of a deterministic parameter; a generalization of the Cramér-Rao bound, it is both tighter and more widely applicable, but usually harder to compute.


Hammersley-Chapman-Robbins bound

Hammersley-Chapman-Robbins bound (plural Hammersley-Chapman-Robbins bounds)

Chapman-Robbins bound
Chapman-Robbins bound#English

(statistics) Synonym of Chapman-Robbins bound


Cramér-Rao bound

Cramér-Rao bound (plural Cramér-Rao bounds)

Named after Harald Cramér and Calyampudi Radhakrishna Rao, who (among others) independently derived it in the 1940s.

(estimation theory, statistics) A lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter.


hazard ratio

(statistics, medicine) A measure of the chance of an event in one group compared to that of another at a particular time or over a subset of a study's time; the ratio between two groups' hazard rates.

Ausfallrate

instantaneous risk of an intervention over a study time period


kitchen sink regression

kitchen sink regression (plural kitchen sink regressions)

(statistics, derogatory) A statistical regression which uses many possible independent variables to attempt to explain variance in a dependent variable.


cocluster

(statistics) A simultaneous cluster of rows and columns.


case fatality rate

case fatality rate (plural case fatality rates)

That 3.4 percent mortality rate, though still fluid, is formidable, even compared next to the case fatality rates (the number of deaths compared to the total number of those diagnosed) for other recent outbreaks.

2020 March 12, Matt Stieb, “Does the Coronavirus Think I’m Old?”, in New York:

(pathology, epidemiology, statistics) A percentage derived by the division of the number of fatalities by the number of confirmed (diagnosed) cases (sufferers) of a disease.

smrtnost

ratio of number of fatalities to number of disease cases


heteroaddition

(statistics) The effect of the addition of two or more different agents


isoaddition

(statistics) The effect of the addition of two or more similar agents


KF

(statistics) Initialism of Kalman filter.


multinormality

(statistics) The condition of being multinormal


central moment

(statistics) A moment of a probability distribution of a random variable about the random variable's mean.

العَزْم المَرْكَزِيّ

statistics: moment of a probability distribution


frequency distribution

frequency distribution (plural frequency distributions)

(statistics) a structured representation that summarizes how often values or categories occur within a dataset by organizing quantitative data into class intervals and categorizing qualitative data into distinct groups, thus revealing patterns, trends, and distributions, often showed in a list, table, or graph that displays the frequency of various outcomes in a sample.


Metropolis-Hastings algorithm

the Metropolis-Hastings algorithm (canonical)

Named after Nicholas Metropolis and W. K. Hastings.

(statistics) A Markov chain Monte Carlo method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.


midcorrelation

(statistics) A correlation between the medians of two populations


Behrens-Fisher problem

Behrens-Fisher problem (plural Behrens-Fisher problems)

Named after Walter Behrens and Ronald Fisher.

(statistics) The problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.


pseudopopulation

LL-Q1860 (eng)-Flame, not lame-pseudopopulation.wav

(statistics) A subset of a population used in simulations


statistically significant

en-adj

statistically significant (comparative more statistically significant, superlative most statistically significant)

more statistically significant (comparative)
most statistically significant (superlative)

(regarding p-values): Coined by Sir Ronald Aylmer Fisher

Data were tested for equiproportionality and Chi-square test associated p-value is reported when the difference is statistically significant.

2016 January 13, “USP2-45 Is a Circadian Clock Output Effector Regulating Calcium Absorption at the Post-Translational Level”, in PLOS ONE, →DOI:

(statistics) Having a p-value of 0.05 or less (having a probability of 5% or less of occurring by random chance)


platykurtotic

platykurtotic (comparative more platykurtotic, superlative most platykurtotic)

more platykurtotic (comparative)
most platykurtotic (superlative)


GLM

generalized linear model
generalized linear model#English

(statistics) Initialism of generalized linear model.


diffogram

(statistics) A diagram that uses diagonal lines to display the results of multiple pairwise difference of means tests.


excess kurtosis

en-noun

excess kurtosis (plural excess kurtoses)

(statistics) Kurtosis minus 3; the difference between the kurtosis of a given distribution and the kurtosis of a normal distribution.


Mann-Whitney U test

Mann-Whitney U test (plural Mann-Whitney U tests)

Developed by Henry B. Mann and Donald R. Whitney, who described it in a 1947 paper.

(statistics) A nonparametric test of the null hypothesis that the probability that a randomly selected value from one population is less than a randomly selected value from a second population is equal to the probability of being greater. It can be used to investigate whether two independent samples were selected from populations having the same distribution.


snowball sampling

(sociology, statistics) A nonprobability sampling technique where existing study subjects recruit future subjects from among their acquaintances.


pentadal

(statistics) Of or related to a 5-year period.


Tukey's range test

(statistics) A single-step multiple-comparison procedure and statistical test that can be used to find means that are significantly different from each other.


Tukey lambda distribution

Tukey lambda distribution (plural Tukey lambda distributions)

(statistics) A continuous, symmetric probability distribution defined in terms of its quantile function, typically used to identify an appropriate distribution.


medcouple

From med (“median”) + couple, as the median of a kernel function over pairs ("couples") of data points. The original paper also introduced a similar concept medtriple that has not seen wide use.

(statistics) A scaled median difference between the two halves of a distribution.


algebraic statistics

հանրահաշվական վիճակագրություն

discipline that uses algebra in the study of statistics

That workshop was built on the algebraic statistics paradigm, which is that statistical models for discrete data can be regarded as solutions to systems of polynomial equations.

2005, Lior Pachter, Bernd Sturmfels, editors, Algebraic Statistics for Computational Biology, Volume 13, Cambridge University Press, page ix:

Algebraic statistics is concerned with the development of techniques in algebraic geometry, commutative algebra, and combinatorics, to address problems in statistics and its applications.

2009, Mathias Drton, Bernd Sturmfels, Seth Sullivant, Lectures on Algebraic Statistics, Springer (Birkhäuser), page vii:

We present a brief review of classical experimental design in the spirit of algebraic statistics.

2010, G. Pistone, E. Riccomagno, M. P. Rogantin, “5: Methods in Algebraic Statistics for the Design of Experiments”, in Luc Pronzato, Anatoly Zhigljavsky, editors, Optimal Design and Related Areas in Optimization and Statistics, Springer,, page 97:

mathematical statistics
mathematical statistics

(mathematics, statistics) A discipline within mathematical statistics in which algebra is used to describe and analyse problems;

A discipline within mathematical statistics in which algebra is used to describe and analyse problems;
specifically, the use of algebraic geometry and commutative algebra in statistics.


heterokurtosis

(statistics) The property of a series of random variables of not every variable having the same finite kurtosis


homokurtosis

2010, Jeffrey M. Wooldridge, Econometric Analysis of Cross-Section and Panel Data (2nd ed.), MIT Press
In terms of the original error u_i, this assumption implies that E(u_i⁴∣ mathbf xᵢ)= mathit constant≡κ² under H_0. This is called the homokurtosis (constant conditional fourth moment) assumption. Homokurtosis always holds when u is independent of mathbf x, but there are conditional distributions for which E(u∣ mathbf x)=0 and Var(u∣ mathbf x)=σ² but E(u⁴∣ mathbf x)=0 depends on mathbf x.

(statistics) The property of a series of random variables of every variable having the same finite kurtosis


heterokurtosis-robust

en-adj

heterokurtosis-robust (comparative more heterokurtosis-robust, superlative most heterokurtosis-robust)

more heterokurtosis-robust (comparative)
most heterokurtosis-robust (superlative)

This test […] is sometimes called a heterokurtosis-robust test for heteroskedasticity.

2010, Jeffrey M. Wooldridge, Econometric Analysis of Cross Section and Panel Data, 2nd edition, The MIT Press, page 141:

(statistics) Of an estimator or series of estimators: robust in the presence of heterokurtosis


heteroscedasticity-robust

heteroscedasticity-robust (comparative more heteroscedasticity-robust, superlative most heteroscedasticity-robust)

more heteroscedasticity-robust (comparative)
most heteroscedasticity-robust (superlative)

(statistics) Of an estimator or series of estimators: robust in the presence of heteroscedasticity.


data dredging

(sciences, statistics) Synonym of p-hacking


exponential smoothing

en-noun

exponential smoothing (countable and uncountable, plural exponential smoothings)

(statistics) a rule-of-thumb technique for smoothing time series data using the exponential window function.


Rao-Blackwellize

en-verb

Rao-Blackwellize (third-person singular simple present Rao-Blackwellizes, present participle Rao-Blackwellizing, simple past and past participle Rao-Blackwellized)

Rao-Blackwellizes (present singular third-person)
Rao-Blackwellizing (participle present)
Rao-Blackwellized (participle past)
Rao-Blackwellized (past)

(transitive, statistics) To apply the Rao–Blackwell theorem to an estimator.


Rao-Blackwellization

en-noun

Rao-Blackwellization (countable and uncountable, plural Rao-Blackwellizations)

(statistics) The procedure of applying the Rao–Blackwell theorem to an estimator.


Rao-Blackwellized

en-adj

Rao-Blackwellized (comparative more Rao-Blackwellized, superlative most Rao-Blackwellized)

more Rao-Blackwellized (comparative)
most Rao-Blackwellized (superlative)

(statistics) Of an estimator, being the result of Rao-Blackwellization.


t-distribution

t-distributions (plural)
t distribution (alternative)

Student's t-distribution
Student's t-distribution#English

(statistics) Ellipsis of Student's t-distribution.


t distribution

t distributions (plural)
t-distribution (alternative)

Student's t distribution
Student's t distribution#English

(statistics) Ellipsis of Student's t distribution.


neutrosophics

(statistics) neutrosophic probability or statistics


underfactorization

LL-Q1860 (eng)-Flame, not lame-underfactorization.wav

(statistics) The use or consideration of too few factors in factor analysis.


mixingness

Mixingness implies ergodicity.

(statistics) The quality or characteristic of being mixing.


GPD

en-noun

GPD (countable and uncountable, plural GPDs)

Generalized Pareto distribution
w:Generalized Pareto distribution

(statistics) Initialism of Generalized Pareto distribution.


rejection sampling

rejection sampling (usually uncountable, plural rejection samplings)

(computational statistics, numerical analysis) A technique used to generate observations from a distribution by repeatedly sampling an approximation function that bounds the distribution everywhere from above and rejecting the samples based on the quotient of the two functions at the sample's location.


ziggurat algorithm

ziggurat algorithm (plural ziggurat algorithms)

(statistics) An algorithm for pseudorandom number sampling, relying on an underlying source of uniformly-distributed random numbers as well as computed tables.


quartimax

(statistics) Describing an orthogonal rotation that maximizes the squared loadings for each variable rather than each factor.


equimax

(statistics) Describing a compromise between varimax and quartimax criteria.


tabulating machine

tabulating machine (plural tabulating machines)

(accounting, computing, statistics, historical) An electromechanical machine used to summarise information and perform accounting calculations.


concept drift

concept drift (countable and uncountable, plural concept drifts)

Concept refers to the hidden relationship between the inputs and outputs of the model.

Regarding collection usage, frecency metrics are employed, combining frequency and recency, to effectively capture concept drift and temporal trends.

2010, Mounia Lalmas et al., editors, Research and Advanced Technology for Digital Libraries […] , Springer, →ISBN, page 544:

Concept drift is an important issue to be considered in data stream mining. In a real environment, the data distribution is constantly changing, and the model needs to be continuously updated to adapt to the new environment.

2020, Zhiwen Yu et al., editors, Green, Pervasive, and Cloud Computing […] , Springer Nature, →ISBN, page 115:

(statistics, machine learning) The tendency of a statistical model to become less and less accurate over time in real-world conditions.


MAE

MAE (countable and uncountable, plural MAEs)

Coordinate term: MSE

mean absolute error
w:mean absolute error

(statistics) Initialism of mean absolute error.


Gibbs measure

(statistics) A generalization of the canonical ensemble to infinite systems, giving the probability of a given system being in a given state (or, equivalently, of a given random variable having a given value).


Gibbs state

(statistics) An equilibrium probability distribution which remains invariant under future evolution of the system.


observational error

observational error (plural observational errors)

(statistics) The difference between a measured value of a quantity and its true value.


coefficient of alienation

coefficient of alienation (plural coefficients of alienation)

(statistics) A numerical measure of the lack of relationship between variables.


coefficient of determination

coefficient of determination (plural coefficients of determination)

independent variable
independent variable

(statistics) The proportion of the variation in the dependent variable that is predictable from the independent variable(s), providing a measure of how well the observed outcomes are replicated by a model.


GEV

(statistics) Initialism of generalized extreme value.


Gumbel distribution

Gumbel distribution (plural Gumbel distributions)

Named after Emil Julius Gumbel (1891–1966), who described the distribution.

(probability theory, statistics) A model of the distribution of the maximum (or the minimum) of a number of samples of various distributions.


linear regression

linear regression (plural linear regressions)

(statistics) A linear equation for deriving a single predicted value from one or more known explanatory values.


sequential probability ratio test

sequential probability ratio test (plural sequential probability ratio tests)

sequential probability ratio tests (plural)

(statistics) A type of statistical test used to evaluate a hypothesis to within a specified level of confidence while minimizing the number of samples required to come to a decision.


Berkson's paradox

(probability, statistics) A counterintuitive result arising in statistical tests of proportions when there is an ascertainment bias inherent in a study design.


gambler's ruin

(statistics) The fact that a gambler playing a game with negative expected value will eventually go broke, regardless of the betting system used.


z-test

(statistics) Any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.


LRL

Coordinate term: URL

(medicine, statistics) Initialism of lower reference limit.


central tendency

central tendency (plural central tendencies)

Central tendency describes a single number that aims to give you a sense of the most representative value in your data. In other words, if you were to choose one number that would best represent all the numbers on a variable in your data set, this would be it.

2013, Donncha Hanna, Martin Dempster, Psychology Statistics For Dummies, John Wiley & Sons, →ISBN, page 54:

(statistics) A central or typical value for a probability distribution.


Bessel's correction

(statistics) The use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample. This corrects the bias in the estimation of the population variance and partially corrects the bias in the estimation of the population standard deviation, but often also increases the mean squared error in these estimations.


sojourn time

sojourn time (countable and uncountable, plural sojourn times)

(probability theory, statistics) The time spent in a state of a stochastic process.


cumulative error

cumulative error (plural cumulative errors)

Rounding the results of intermediate calculations introduces cumulative error in the final answer.

(statistics) A statistical or measurement error that compounds with further calculation, analysis, etc.


equinormality

(statistics) Having a normal distribution and equal variance.


IPD

IPD (countable and uncountable, plural IPDs)

(statistics) Initialism of individual participant data.


time-use survey

time-use survey (plural time-use surveys)

(economics, statistics) A statistical survey which aims to report data, on average, on the manners and ways of people spending their time.


time-space grid

time-space grid (plural time-space grids)

(sciences, statistics) The combination of a geographical area divided into equal sectors and a regular time interval.


Markov renewal process

Markov renewal process (countable and uncountable, plural Markov renewal processes)

(mathematics, probability theory, statistics) A class of random processes that generalize the class of Markov jump processes.


ceiling effect

(statistics) The phenomenon where an independent variable no longer has an effect on a dependent variable, or the level above which variance in an independent variable is no longer measurable.


cohort effect

(statistics, social sciences) The phenomenon in which research outcomes may depend on the characteristics and experiences shared within each particular cohort.


floor effect

Coordinate term: ceiling effect

(statistics) The phenomenon in which a data-gathering instrument has a lower limit to the data values it can reliably specify.


Gerschenkron effect

Gerschenkron effect (plural Gerschenkron effects)

Named after Alexander Gerschenkron who developed the idea.

(economics, statistics) The theory that changing the base year for an index determines the growth rate of the index.


Anderson-Darling test

Anderson-Darling test (plural Anderson-Darling tests)

Named after Theodore Wilbur Anderson and Donald Allan Darling who invented it in 1952.

(statistics) A statistical test of whether a given sample of data is drawn from a given probability distribution.

Donald Allan Darling
Theodore Wilbur Anderson


Spiders Georg

From a 2013 Tumblr post by Max Lavergne inventing a satirical explanation for a popular urban legend claiming the average person swallows three spiders a year: "Spiders Georg, who lives in cave & eats over 10,000 [spiders] each day, is an outlier adn^([sic]) should not have been counted."

“The consistent pattern is that the most common number is zero. Most people do not transmit,” said Jamie Lloyd-Smith, another infectious disease specialist, sounding a bit like the statistics meme Spiders Georg.

2020 June 3, Lissa Harris, Phillip Pantuso, Roger Hannigan Gilson, “Coronavirus Roundup: Superspreaders May Account for Most COVID-19 Transmission”, in The River:

He's officially become the "Spiders Georg" of world leaders.

2023 August 15, Madison Hall, “The average US president has been charged with 2 felonies now, thanks to Trump”, in Business Insider:

On the day the post was made, the world population was 7,252,764,262 [9]. That would mean that Spiders Georg would have to eat approximately 2.176x10¹⁰ spiders per day.

2024, Kai Jac Cordes, “How Many Spiders Would Spiders Georg Have To Eat?”, in Journal of Interdisciplinary Science Topics, volume XCI, number 24:

(Internet slang, humorous, statistics) A notional extreme outlier in a population, originally characterized as a cave-dwelling hermit who eats 10,000 spiders per day and thus skews the statistical average for all humanity.


data collection

(statistics) The process of gathering and measuring information on targeted variables in an established system.


SSU

SSU (countable and uncountable, plural SSUes)

(statistics) Initialism of secondary sampling unit, a sampling unit in the second stage of a polyetapic sampling.


contactive

In a complex distribution, if both of the contactive units are chains, there can be a reduction in the total of inferences only if one of the chains is in a simple distribution with a third chain and the interval is unoccupied.

2018, Isidore Dyen, Linguistic Subgrouping and Lexicostatistics, page 73:

(statistics) Contiguous but not coordinated


y-o-y

(statistics) Initialism of year-over-year or year-on-year.


within one sigma

(statistics) Describing the range from the mean, plus or minus one standard deviation, usually covering 68% of the data points in a normal distribution.


FWER

(statistics) Initialism of familywise error rate.


FWE

(statistics) Initialism of familywise error.


double descent

(statistics, machine learning) The phenomenon where a model with few parameters and a model with many parameters have a small test error, but a model whose number of parameters is about the same as the number of data points used to train the model will have a large error.


Box-Cox distribution

Box-Cox distribution (plural Box-Cox distributions)

Box-Cox transformation
Box-Cox transformation

(statistics) The distribution of a random variable X for which the Box-Cox transformation on X follows a truncated normal distribution.


Fisher-Tippett-Gnedenko theorem

the Fisher-Tippett-Gnedenko theorem (canonical)

extreme value theory
extreme value theory

Fréchet distribution
Fréchet distribution

Weibull distribution
Weibull distribution

(statistics) A general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of three possible distribution families: the Gumbel distribution, the Fréchet distribution, or the Weibull distribution.


path analysis

The authors take care not to exceed the limitations of their method. Because path analysis can be used only to test existing notions, not to propose new hypotheses, the researchers cannot investigate possible biological pathways to homosexuality. But they can — and do — rule out nearly all of what must be an exhaustive array of social and psychological influences.

1982 February 6, Larry Goldsmith, “Science vs. Real Life”, in Gay Community News, volume 9, number 28, page 12:


p-hack

en-verb

p-hack (third-person singular simple present p-hacks, present participle p-hacking, simple past and past participle p-hacked)

p-hacks (present singular third-person)
p-hacking (participle present)
p-hacked (participle past)
p-hacked (past)

(sciences, statistics) To engage in p-hacking.


metalog

(statistics) A flexible continuous probability distribution designed for ease of use.


iid-ness

(statistics, probability theory) The state of being iid (independent and identically distributed).


LOESS

Locally weighted regression, or loess, is a procedure for fitting a regression surface to data through multivariate smoothing.

1986, William S. Cleveland and Susan J. Delvin, “Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting”, in Journal of the American Statistical Association, volume 83, number 403, page 596:

locally estimated scatterplot smoothing#English

(statistics) Acronym of locally estimated scatterplot smoothing.


pivotal quantity

en-noun

pivotal quantity (plural pivotal quantities)

(statistics) A random variable transformed such that its distribution does not depend on unknown parameters.


snowball sample

snowball sample (plural snowball samples)

(sociology, statistics) A sample obtained through the existing social networks of its participants.