''sample distribution''
...s to every value $ X_{k} $ the probability $ \dfrac{1}{n} $. The empirical distribution function $ F_{n} $ is the step-function with steps of multiples of $ \dfrac
5 KB (778 words) - 04:08, 22 June 2017
be a random variable having a continuous and strictly increasing distribution function $ F $.
has a uniform distribution on the interval $ [ 0 , 1 ] $,
4 KB (562 words) - 20:33, 16 January 2024
...tatistical problem connected with the study of other parameters of a given distribution. More precisely, for a realization of a random variable $ X $,
...to make a statistical inference not depending on these parameters. In the theory of statistical hypothesis testing one often achieves this by narrowing the
2 KB (341 words) - 08:03, 6 June 2020
...al distribution]]. It is used as a certain measure of the deviation of the distribution in question from the normal one. The excess $ \gamma _ {2} $
is the second Pearson coefficient (cf. [[Pearson distribution|Pearson distribution]]), and $ \mu _ {2} $
4 KB (594 words) - 17:18, 6 January 2024
distribution''
The [[Probability distribution|probability distribution]] of the random variable
3 KB (396 words) - 20:47, 22 January 2024
''in probability theory and mathematical statistics''
Theorems that establish a connection between the type of the distribution of random variables or random vectors and certain general properties of fun
3 KB (414 words) - 16:43, 4 June 2020
$#C+1 = 36 : ~/encyclopedia/old_files/data/H048/H.0408430 Hypergeometric distribution
The probability distribution defined by the formula
4 KB (602 words) - 22:11, 5 June 2020
...h that the distributions of $X_2$ and $BX_1+A$ coincide. The corresponding distribution functions are then connected by the relation
Thus the set of distribution functions decomposes into mutually disjoint types. For example, all normal
4 KB (649 words) - 14:15, 17 April 2014
...yclopedia/old_files/data/M064/M.0604610 Moments, method of (in probability theory)
A method for determining a [[Probability distribution|probability distribution]] by its moments (cf. [[Moment|Moment]]). Theoretically the method of momen
4 KB (609 words) - 16:25, 6 January 2024
$#C+1 = 42 : ~/encyclopedia/old_files/data/I052/I.0502550 Involutive distribution
A $ p $-dimensional distribution (or a differential system of dimension $ p $)
3 KB (378 words) - 10:11, 21 March 2022
$#C+1 = 35 : ~/encyclopedia/old_files/data/W097/W.0907370 Weibull distribution
A particular [[Probability distribution|probability distribution]] of random variables $ X _ {w} $,
5 KB (690 words) - 06:37, 7 October 2023
...istributions (cf. [[Infinitely-divisible distribution|Infinitely-divisible distribution]]). If the distributions of $ S _ {n} $
converge to a limit distribution, $ k _ {n} \rightarrow \infty $,
2 KB (324 words) - 18:48, 5 April 2020
...ocess with independent increments is called homogeneous if the probability distribution of $ X ( \alpha + h ) - X ( \alpha ) $,
...can only have discontinuities of the first kind, with probability one. The distribution of the values of such a process for any $ t $
3 KB (473 words) - 08:23, 6 June 2020
$#C+1 = 51 : ~/encyclopedia/old_files/data/P073/P.0703280 Poisson distribution
[[Category:Distribution theory]]
7 KB (971 words) - 17:34, 6 January 2024
$#C+1 = 71 : ~/encyclopedia/old_files/data/P073/P.0703540 P\Aeolya distribution
The probability distribution of a random variable $ X _ {n} $
6 KB (838 words) - 08:08, 6 June 2020
$#C+1 = 18 : ~/encyclopedia/old_files/data/E036/E.0306900 Exponential distribution
[[Category:Distribution theory]]
3 KB (485 words) - 19:23, 10 April 2024
...ble if it lies in the region of values of the [[Normal distribution|normal distribution]] of a random variable at a distance from its [[Mathematical expectation|ma
where $\Phi(\cdot)$ is the distribution function of the standard normal law; whence, in particular, for $k=3$ it fo
1 KB (223 words) - 00:44, 24 December 2018
One of the basic concepts in [[Probability theory|probability theory]] and [[Mathematical statistics|mathematical statistics]]. In the modern ap
..., proved to be too general in the course of the further development of the theory and was replaced by more restrictive ones in order to exclude some "patholo
8 KB (1,003 words) - 21:59, 21 November 2018
$#C+1 = 50 : ~/encyclopedia/old_files/data/S087/S.0807110 Stable distribution
[[Category:Distribution theory]]
6 KB (799 words) - 18:06, 14 October 2023
...R><TD valign="top">[a3]</TD> <TD valign="top"> A.J. Lee, "U-statistics. Theory and practice" , ''Statistics textbooks and monographs'' , '''110''' , M. De
4 KB (507 words) - 22:10, 5 June 2020