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If X has a standard uniform distribution, then by the inverse transform sampling method, Y = − λ −1 ln(X) has an exponential distribution with (rate) parameter λ. If X has a standard uniform distribution, then Y = X n has a beta distribution with parameters (1/n,1). As such, The Irwin–Hall distribution is the sum of n i.i.d. U(0,1 ...
) of real numbers is said to be completely uniformly distributed mod 1 it is -uniformly distributed for each natural number . For example, the sequence ( α , 2 α , … ) {\displaystyle (\alpha ,2\alpha ,\dots )} is uniformly distributed mod 1 (or 1-uniformly distributed) for any irrational number α {\displaystyle \alpha } , but is never even ...
might hold, given some general sequence b k. One noteworthy result is that the sequence 2 k a mod 1 is uniformly distributed for almost all, but not all, irrational a. Similarly, for the sequence b k = 2 k a, for every irrational a, and almost all x, there exists a function ƒ for which the sum diverges.
Uniform distribution may refer to: Continuous uniform distribution; Discrete uniform distribution; Uniform distribution (ecology) Equidistributed sequence; See also.
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/n. Intuitively, a discrete uniform distribution is "a known, finite number ...
Note that under this definition the uniform distribution is unimodal, [4] as well as any other distribution in which the maximum distribution is achieved for a range of values, e.g. trapezoidal distribution. Usually this definition allows for a discontinuity at the mode; usually in a continuous distribution the probability of any single value ...
In probability and statistics, the Irwin–Hall distribution, named after Joseph Oscar Irwin and Philip Hall, is a probability distribution for a random variable defined as the sum of a number of independent random variables, each having a uniform distribution. [1] For this reason it is also known as the uniform sum distribution.
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...