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It is not immediately clear from the definition how exotic a distribution might be. To answer this question, it is instructive to see distributions built up from a smaller space, namely the space of continuous functions. Roughly, any distribution is locally a (multiple) derivative of a continuous function.
The mathematical sense of the term is from 1718. In the 18th century, the term chance was also used in the mathematical sense of "probability" (and probability theory was called Doctrine of Chances). This word is ultimately from Latin cadentia, i.e. "a fall, case".
Probability theory or probability calculus is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.
This distribution was first referred to as the normal distribution by C. S. Peirce in 1873 who was studying measurement errors when an object was dropped onto a wooden base. [18] He chose the term normal because of its frequent occurrence in naturally occurring variables.
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]
Purse distribution, in a horse race, the distribution of winnings among the highest finishers; Record distribution, process of shipping and promoting record labels; Font distribution, the units in which metal type is sold, containing relative proportions of letters appropriate for a given language; Distribution (bridge), a term in the bridge ...
In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function. The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfying [1]