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If the uniform distributions have the same width w, the result is a triangular distribution, symmetric about its mean, on the support [a+c,a+c+2w]. The sum of two independent, equally distributed, uniform distributions U 1 (a,b)+U 2 (a,b) yields a symmetric triangular distribution on the support [2a,2b].
Uniform distribution may refer to: Continuous uniform distribution; Discrete uniform distribution; Uniform distribution (ecology) Equidistributed sequence; See also.
As it turns out, uniformly distributed measures are very rigid objects. On any "decent" metric space, the uniformly distributed measures form a one-parameter linearly dependent family: Let μ and ν be uniformly distributed Borel regular measures on a separable metric space (X, d). Then there is a constant c such that μ = cν.
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.
) 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 ...
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.
Let be the product of two independent variables = each uniformly distributed on the interval [0,1], possibly the outcome of a copula transformation. As noted in "Lognormal Distributions" above, PDF convolution operations in the Log domain correspond to the product of sample values in the original domain.
A chart showing a uniform distribution. In 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 the same probability distribution as the others and all are mutually independent. [1]