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The birthday problem has been generalized to consider an arbitrary number of types. [20] In the simplest extension there are two types of people, say m men and n women, and the problem becomes characterizing the probability of a shared birthday between at least one man and one woman. (Shared birthdays between two men or two women do not count.)
The name is based on the birthday paradox. Choose m birthdays in a year of n days. List the spacings between the birthdays. If j is the number of values that occur more than once in that list, then j is asymptotically Poisson-distributed with mean m 3 / (4n).
In some cases, a permutation test based on a properly studentized statistic can be asymptotically exact even when the exchangeability assumption is violated. [8] Bootstrap-based tests can test with the null hypothesis H 0 : F ≠ G {\displaystyle H_{0}:F\neq G} and, therefore, are suited for performing equivalence testing .
Enumerations of specific permutation classes; Factorial. Falling factorial; Permutation matrix. Generalized permutation matrix; Inversion (discrete mathematics) Major index; Ménage problem; Permutation graph; Permutation pattern; Permutation polynomial; Permutohedron; Rencontres numbers; Robinson–Schensted correspondence; Sum of permutations ...
Several parallel shuffle algorithms, based on Fisher—Yates have been developed. In 1990, Anderson developed a parallel version for machines with a small number of processors accessing shared memory. [11] The algorithm generates a random permutations uniformly so long as the hardware operates in a fair manner.
A logical spreadsheet is a spreadsheet in which formulas take the form of logical constraints rather than function definitions.. In traditional spreadsheet systems, such as Excel, cells are partitioned into "directly specified" cells and "computed" cells and the formulas used to specify the values of computed cells are "functional", i.e. for every combination of values of the directly ...
In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.
A sorting algorithm is stable if whenever there are two records R and S with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list. When equal elements are indistinguishable, such as with integers, or more generally, any data where the entire element is the key, stability is not an issue.