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...

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

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...

(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...

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...

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...

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

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...

(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...

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

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...

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

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

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

"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...

statistics use formal definitions of randomness, typically assuming that there is some 'objective' probability distribution. In statistics, a random variable...

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

In probability theory and statistics, covariance is a measure of the joint variability of two random variables. The sign of the covariance, therefore,...

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...

their restrictions to specific degrees are used to compute random permutation statistics. There are two useful restrictions of this operator, namely...

In statistics, the mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which...