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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 ...
If k exemplars are chosen (without replacement) from a discrete uniform distribution over the set {1, 2, ..., N} with unknown upper bound N, the MVUE for N is +, where m is the sample maximum. This is a scaled and shifted (so unbiased) transform of the sample maximum, which is a sufficient and complete statistic.
5.3 Uniform distribution ... and uniformly distributed on the interval [0,θ], then T(X) = max(X ... sufficient estimator is the best estimator of its ...
The problem of estimating the maximum of a discrete uniform distribution on the integer interval [,] from a sample of k observations is commonly known as the German tank problem, following the practical application of this maximum estimation problem, during World War II, by Allied forces seeking to estimate German tank production.
Given u and v, independent and uniformly distributed in the closed interval [−1, +1], set s = R 2 = u 2 + v 2. If s = 0 or s ≥ 1 , discard u and v , and try another pair ( u , v ) . Because u and v are uniformly distributed and because only points within the unit circle have been admitted, the values of s will be uniformly distributed in ...
0, α, 2α, 3α, 4α, ... is equidistributed modulo 1. [3] More generally, if p is a polynomial with at least one coefficient other than the constant term irrational then the sequence p(n) is uniformly distributed modulo 1. This was proven by Weyl and is an application of van der Corput's difference theorem. [4]
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For example, if x had 10 values from the natural numbers: [1,2,3...,10], then we can imagine x to be a Discrete uniform distribution. Under this interpretation all x i {\displaystyle x_{i}} have the same expectation and some positive variance.