The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms...

A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a...

random forests, in particular: Using out-of-bag error as an estimate of the generalization error. Measuring variable importance through permutation....

statistics, resampling is the creation of new samples based on one observed sample. Resampling methods are: Permutation tests (also re-randomization tests)...

A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more...

mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus...

probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has...

variability than the arithmetic mean of a simple random sample of the population. In computational statistics, stratified sampling is a method of variance...

each of its faces. Less simply, a random permutation is a permutation generated uniformly randomly from the permutations of a given set and a uniform spanning...

drawers independently at random. Prisoner's dilemma Three prisoners problem Unexpected hanging paradox Random permutation statistics Golomb–Dickman constant...

element Random field Random function Random graph Random matrix Random measure Random multinomial logit Random naive Bayes Random permutation statistics Random...

the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n {\displaystyle...

(univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination...

In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown...

(xi, yi), randomly redefine the pairs to create a new data set (xi, yi′), where the i′ are a permutation of the set {1,...,n}. The permutation i′ is selected...

exchangeable sequence of random variables is a finite or infinite sequence X1, X2, X3, ... of random variables such that for any finite permutation σ of the indices...

theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable...

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation...

into no more than m parts. This is proved in the article on random permutation statistics, although the notation is a bit different. The Stirling numbers...

An overview of the most important results may be found at random permutation statistics. Dixon & Mortimer 1996, pg. 2, section 1.2 Symmetric groups...

between approximate randomization and permutation tests. An approximate randomization test is based on a specified subset of all permutations (which entails...

"Bootstrap methods and permutation tests" (PDF). In David S. Moore, George McCabe (eds.). Introduction to the Practice of Statistics. software. Archived...

Dickman, is a mathematical constant, which arises in the theory of random permutations and in number theory. Its value is λ = 0.62432998854355087099293638310083724...

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as...

Concentration inequality Convergence of random variables Computational statistics Markov chain Monte Carlo Bootstrapping (statistics) Jackknife resampling Integrated...

235: Random permutation". Communications of the ACM. 7 (7): 420. doi:10.1145/364520.364540. Robert Moscowitz (July 12, 1999). "Privacy's Random Nature"...

possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events...

definition of expected value for arbitrary real-valued random variables). An equivalent phrasing uses a random variable X distributed according to F: P ⁡ ( X...

statistics Ratio estimator Replication (statistics) Random-sampling mechanism Resampling (statistics) Pseudo-random number sampling Sample size determination...

taken from Kendall's Advanced Theory of Statistics. Statistical hypotheses concern the behavior of observable random variables.... For example, the hypothesis...