|
Kolmogorov–Zurbenko Filter
Within statistics, the Kolmogorov–Zurbenko (KZ) filter was first proposed by A. N. Kolmogorov and formally defined by Zurbenko.I. Zurbenko. The Spectral Analysis of Time Series. North-Holland Series in Statistics and Probability, 1986. It is a series of iterations of a moving average filter of length ''m'', where ''m'' is a positive, odd integer. The KZ filter belongs to the class of low-pass filters. The KZ filter has two parameters, the length ''m'' of the moving average window and the number of iterations ''k'' of the moving average itself. It also can be considered as a special window function designed to eliminate spectral leakage. Background A. N. Kolmogorov had the original idea for the KZ filter during a study of turbulence in the Pacific Ocean. Kolmogorov had just received the International Balzan Prize for his Turbulence#Kolmogorov.27s theory of 1941, law of 5/3 in the energy spectra of turbulence. Surprisingly the 5/3 law was not obeyed in the Pacific Ocean, causing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elizabeth Scott (mathematician)
Elizabeth Leonard Scott (November 23, 1917 – December 20, 1988) was an American mathematician specializing in statistics. Scott was born in Fort Sill, Oklahoma. Her family moved to Berkeley, California when she was 4 years old. She attended the University of California, Berkeley where she studied astronomy. She earned her Ph.D. in 1949 in astronomy, and received a permanent position in the Department of Mathematics at Berkeley in 1951. She wrote over 30 papers on astronomy and 30 on weather modification research analysis, incorporating and expanding the use of statistical analyses in these fields. She also used statistics to promote equal opportunities and equal pay for female academics. In 1957 Scott noted a bias in the observation of galaxy clusters. She noticed that for an observer to find a very distant cluster, it must contain brighter-than-normal galaxies and must also contain a large number of galaxies. She proposed a correction formula to adjust for (what came to b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-correlation of and , or and . For complex-valued fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution (mathematics)
Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions than classical solutions, or where appropriate classical solutions may not exist. Distributions are also important in physics and engineering where many problems naturally lead to differential equations whose solutions or initial conditions are singular, such as the Dirac delta function. A function f is normally thought of as on the in the function domain by "sending" a point x in its domain to the point f(x). Instead of acting on points, distribution theory reinterp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves variables, they may also be called parameters. For example, the polynomial 2x^2-x+3 has coefficients 2, −1, and 3, and the powers of the variable x in the polynomial ax^2+bx+c have coefficient parameters a, b, and c. The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter ''c'', respectively. The coefficient attached to the highest degree of the variable in a polynomial is referred to as the leading coefficient. For example, in the expressions above, the leading coefficients are 2 and ''a'', respectively. Terminology and definition In mathematics, a coefficient is a multiplicative factor in some term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry. Etymology The word ''polynomial'' joins tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and the visco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''fore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real-valued Function
In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain. Real-valued functions of a real variable (commonly called ''real functions'') and real-valued functions of several real variables are the main object of study of calculus and, more generally, real analysis. In particular, many function spaces consist of real-valued functions. Algebraic structure Let (X,) be the set of all functions from a set to real numbers \mathbb R. Because \mathbb R is a field, (X,) may be turned into a vector space and a commutative algebra over the reals with the following operations: *f+g: x \mapsto f(x) + g(x) – vector addition *\mathbf: x \mapsto 0 – additive identity *c f: x \mapsto c f(x),\quad c \in \mathbb R – scalar multiplication *f g: x \mapsto f(x)g(x) – pointwise multiplication These operations extend to partial functions from to \mathbb R, with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emanuel Parzen
Emanuel Parzen (April 21, 1929 – February 6, 2016) was an American statistician. He worked and published on signal detection theory and time series analysis, where he pioneered the use of kernel density estimation (also known as the Parzen window in his honor). Parzen was the recipient of the 1994 Samuel S. Wilks Memorial Medal of the American Statistical Association. Biography Parzen attended Bronx High School of Science. He then matriculated to Harvard, where he earned his undergraduate degree in mathematics in 1949. From there, he went on to Berkeley, earning his master and doctorate degrees in mathematics in 1951 and 1953, respectively. His dissertation, "On Uniform Convergence of Families of Sequences of Random Variables", was written under Michel Loève. Parzen went directly into academia after graduate school, first serving as a research scientist in the physics department and assistant professor of mathematical statistics at Columbia University. He left there in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilfrid Dixon
Wilfrid Joseph Dixon (December 13, 1915 – September 20, 2008) was an American mathematician and statistician. He made notable contributions to nonparametric statistics, statistical education and experimental design. A native of Portland, Oregon, Dixon received a bachelor's degree in mathematics from Oregon State College in 1938. He continued his graduate studies at the University of Wisconsin–Madison, where he earned a master's degree in 1939. Under supervision of Samuel S. Wilks, he then earned a Ph.D. in mathematical statistics from Princeton in 1944. During World War II, he was an operations analyst on Guam. Dixon was on the faculties at Oklahoma (1942–1943), Oregon (1946–1955), and UCLA (1955–1986, then emeritus). While at Oregon, Dixon (together with A.M. Mood) described and provided theory and estimation methods for the adaptive Up-and-Down experimental design, which was new and poorly documented at the time. This article became the cornerstone publication ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Robbins
Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of '' What is Mathematics?'', a popularization that is still () in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping). Biography Robbins was born in New Castle, Pennsylvania. As an undergrad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
