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...c. When considering the statistical problem of discrimination, S. Kullback and R.A. Leibler [[#References|[a13]]] introduced a measure of the "distance"
9 KB (1,370 words) - 22:15, 5 June 2020
...uthor(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike Lic
'''STATISTICS IN INSURANCE'''
9 KB (1,305 words) - 09:48, 28 October 2023
...ct, and the natural numerical measure of indefiniteness of an event is its probability.
...e assumption that the methods of encoding the message into an input signal and of decoding the output into a message may vary within wide ranges.
7 KB (993 words) - 17:28, 7 February 2011
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A measure of the linear dependence between one random variable and a certain collection of random variables. More precisely, if $ ( X _ {1}
5 KB (666 words) - 08:02, 6 June 2020
''of stochastic processes and fields''
...odic theory|ergodic theory]] and mixing conditions in [[Probability theory|probability theory]] based on appropriate mixing coefficients measuring the dependence
7 KB (1,086 words) - 06:27, 26 March 2023
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A distance between probability measures, expressed in terms of the [[Hellinger integral|Hellinger integral
3 KB (423 words) - 22:10, 5 June 2020
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and if for some $ n \geq 1 $
5 KB (661 words) - 12:22, 17 January 2021
...re the exposition is based on the concept of a space of elementary events, and where it is stressed that only in this context the notion of a random varia
...quation $P_X(B)=P\{X(\omega)\in B\}$, $B\in\mathcal{B}_1$, is called the [[probability distribution]] of $X$. This measure is uniquely determined by the [[distrib
6 KB (904 words) - 20:43, 1 January 2019
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...rameters of probability laws from results of observations. It was proposed and developed by [[Neyman, Jerzy|J. Neyman]] (see [[#References|[1]]], [[#Refer
8 KB (1,137 words) - 07:29, 24 March 2023
...iance is defined for random variables $X_1$ and $X_2$ with finite variance and is usually denoted by $\cov(X_1, X_2)$. Thus,
If $X_1$ and $X_2$ are independent random variables, then $\cov(X_1, X_2)=0$. The covari
2 KB (232 words) - 10:53, 18 October 2014
$#C+1 = 20 : ~/encyclopedia/old_files/data/R082/R.0802530 Robust statistics
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5 KB (759 words) - 08:12, 6 June 2020
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The probability distribution of a random variable $ X $
5 KB (776 words) - 10:59, 29 May 2020
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and $ \mu _ {3} $
3 KB (461 words) - 07:30, 26 March 2023
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...eed for the introduction of such a concept arose as early as 1955 or 1956, and it was at that time that Le Cam selected the name of "contiguity" , with t
15 KB (2,180 words) - 17:43, 1 July 2020
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The continuous probability distribution, concentrated on $ ( 0 , \infty ) $,
4 KB (482 words) - 22:17, 5 June 2020
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...termination of functions of given arbitrary random variables for which the probability distributions possess given properties.
4 KB (562 words) - 20:33, 16 January 2024
...uthor(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike Lic
'''Summary.''' Rice, American sociologist and statistician,
6 KB (891 words) - 20:38, 22 September 2016
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...bability]] function on subsets of $\mathcal{S}$, assigning a [[Probability|probability]] to every matrix event.
8 KB (1,193 words) - 17:37, 11 November 2023
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The [[Probability distribution|probability distribution]] of the random variable
3 KB (396 words) - 20:47, 22 January 2024
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...e an unforeseen effect on each of the measurements, both in overestimating and in underestimating results.
12 KB (1,805 words) - 08:11, 21 January 2024