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Asymptotic distribution. In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of statistical ...
Asymptotic analysis. In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared ...
The word Ασύμπτωτος (asymptotos) in Greek means non-coincident and puts strong emphasis on the point that approximation does not turn into coincidence. It is a salient feature of asymptotics, but this property alone does not entirely cover the idea of asymptotics and, etymologically, the term seems to be quite insufficient.
V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. [1] V-statistics are closely related to U-statistics [2][3] (U for "unbiased") introduced by Wassily Hoeffding in 1948. [4] A V-statistic is a statistical function (of a sample) defined by a ...
Plot with random data showing homoscedasticity: at each value of x, the y -value of the dots has about the same variance. Plot with random data showing heteroscedasticity: The variance of the y -values of the dots increases with increasing values of x. In statistics, a sequence of random variables is homoscedastic (/ ˌhoʊmoʊskəˈdæstɪk ...
Asymptotic expansion. In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular ...
known as the asymptotic law of distribution of prime numbers. Adrien-Marie Legendre conjectured in 1797 or 1798 that π (a) is approximated by the function a / (A ln (a) + B), where A and B are unspecified constants. In the second edition of his book on number theory (1808) he then made a more precise conjecture, with A = 1 and B ≈ −1.08366.
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical dispersion.