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31 sty 2024 · In this article, we have characterized the continuous uniform distribution by the characteristic function and observed that these characterizations may serve as a basis for possible...
A Characterization of Uniform Distribution by Joanna CHACHULSKA Presented by Stanisław KWAPIEN´ Summary.Is the Lebesgue measure on [0,1]2a unique product measure on [0,1]2which is transformed again into a product measure on [0,1]2 by the mapping ψ(x,y) = (x,(x+ y) mod 1))? Here a somewhat stronger version of this problem in a probabilistic
1 sty 1993 · Abstract. Let X be a random variable defined on the interval [a,b] with continuous distribution function F. If E (X|X>c)= (b+c)/2 for a<c<b, then X has a uniform distribution on [a,b].
Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias.
A characterization is a certain distributional or statistical property of a statistic or statistics that uniquely determines the associated stochastic model. This chapter provides a brief survey of the huge literature on this topic.
ABSTRACT The univariate distribution uniform on the unit interval [0,1] is important primarily because of the following characterization: Let X be a random variable taking values in [0,1].
It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y −I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete.
