We prove that an absolutely continuous probability distribution with compact support is uniformly distributed if and only if the mean sample spacings resulting from a random sample of size N are all equal for every integer N. We also present a related characterization of uniformity using nonlinear t
CORRELATIONS AND CHARACTERIZATIONS OF THE UNIFORM DISTRIBUTION
โ Scribed by Brown, Timothy C. ;Cartwright, Donald I. ;Eagleson, G. K.
- Book ID
- 115210438
- Publisher
- Wiley (Blackwell Publishing)
- Year
- 1986
- Tongue
- English
- Weight
- 322 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0004-9581
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๐ SIMILAR VOLUMES
Let U and V be independent random variables with continuous density function on the interval (0, 1). We describe families of functions g for which uniformity of U and V is equivalent to uniformity of g(U, V) on (0, 1). These results axe used to prescribe methods for improving the quality of pseudo-r
Denoting by \(X_{(1,} \leqslant X_{t 2} \leqslant \cdots \leqslant X_{(n)}\) the order statistic based on a random sample \(X_{1}, X_{2}, \ldots, X_{n}\) drawn from a distribution \(F\), it is shown that the property " \(E\left(X_{1} \mid X_{(1)}, X_{(n)}\right)=\frac{1}{2}\left(X_{(1)}+X_{(n)}\righ