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Polykay
In statistics, a polykay, or generalised k-statistic, (denoted k_) is a statistic defined as a linear combination of sample moments. Etymology The word ''polykay'' was coined by American mathematician John Tukey in 1956, from ''poly'', "many" or "much", and ''kay'', the phonetic spelling of the letter "k", as in k-statistic In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the '' moments'' of the ....Tukey, J. W. (1956.) "Keeping Moment-Like Computations Simple", ''Ann. Math. Stat.'', 27:37–54. References {{Statistics-stub Symmetric functions Statistical inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Moment
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from to ) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem). In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Americans
Americans are the Citizenship of the United States, citizens and United States nationality law, nationals of the United States, United States of America.; ; Although direct citizens and nationals make up the majority of Americans, many Multiple citizenship, dual citizens, expatriates, and green card, permanent residents could also legally claim American nationality. The United States is home to race and ethnicity in the United States, people of many racial and ethnic origins; consequently, culture of the United States, American culture and Law of the United States, law do not equate nationality with Race (human categorization), race or Ethnic group, ethnicity, but with citizenship and an Oath of Allegiance (United States), oath of permanent allegiance. Overview The majority of Americans or their ancestors Immigration to the United States, immigrated to the United States or are descended from people who were Trans Atlantic Slave Trade, brought as Slavery in the United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term 'bit' and the first published use of the word 'software'. Biography Tukey was born in New Bedford, Massachusetts in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a BA in 1936 and MSc in 1937 in chemistry, from Brown University, before moving to Princeton University, where in 1939 he received a PhD in mathematics after completing a doctoral dissertation titled "On denumerability in topology". During World War II, Tukey worked at the Fire Control Research Office and collaborated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-statistic
In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the '' moments'' of the distribution. Any two probability distributions whose moments are identical will have .... See also k-Statisticon Wolfram MathWorld. Estimator {{statistics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Functions
In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f\left(x_2,x_1\right) for all x_1 and x_2 such that \left(x_1,x_2\right) and \left(x_2,x_1\right) are in the domain of f. The most commonly encountered symmetric functions are polynomial functions, which are given by the symmetric polynomials. A related notion is alternating polynomials, which change sign under an interchange of variables. Aside from polynomial functions, tensors that act as functions of several vectors can be symmetric, and in fact the space of symmetric k-tensors on a vector space V is isomorphic to the space of homogeneous polynomials of degree k on V. Symmetric functions should not be confused with even and odd functions, which have a different sort of symmetry. Symmetrization Given any function f in n variables wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
