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In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence = where is the joint distribution function of two random variables, and and are their marginal distribution functions.
In mathematics, in particular in measure theory, there are different notions of distribution function and it is important to understand the context in which they are used (properties of functions, or properties of measures). Distribution functions (in the sense of measure theory) are a generalization of distribution functions (in the sense of ...
In the theory of probability, the Glivenko–Cantelli theorem (sometimes referred to as the Fundamental Theorem of Statistics), named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, describes the asymptotic behaviour of the empirical distribution function as the number of independent and identically distributed observations grows. [1]
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The f-divergences are probably the best-known way to measure dissimilarity of probability distributions. It has been shown [ 5 ] : sec. 2 that the only functions which are both IPMs and f -divergences are of the form c TV ( P , Q ) {\displaystyle c\,\operatorname {TV} (P,Q)} , where c ∈ [ 0 , ∞ ] {\displaystyle c\in [0,\infty ]} and TV ...
In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculate these confidence intervals, all that is required is an independently and identically distributed (iid) sample from the distribution and known ...
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.