In a common-values election where voters receive a signal about which candidate is superior, suppose there is a small amount of uncertainty about the conditional likelihood of the signalʼs outcome, given the correct candidate. Once this uncertainty is resolved, the signal is i.i.d. across...

Let X1,…,Xn be i.i.d. copies of random variable X where 0E|X|∞ and let X̄=1n∑i=1nXi. One can show that X1−X̄,…,Xn−X̄ are exchangeable, and as a result identically distributed, but not independent. We use this result to prove that for n≥3, X is symmetric about a point if and only...

Using the technique of finding bounds on sets of copulas with particular properties, we compare the distribution of an n-dimensional (n≥3) vector of continuous pairwise independent random variables to the distribution of a similar vector of mutually independent random variables. We examine the...

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X1,X2,…,Xn) without the assumption of continuity and symmetry for each component Xi:P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12   , where allαi≥0 are special...

Two stochastic representations of multivariate geometric distributions are analyzed, both are obtained by lifting the lack-of-memory (LM) property of the univariate geometric law to the multivariate case. On the one hand, the narrow-sense multivariate geometric law can be considered a discrete...

We study Hoeffding decomposable exchangeable sequences with values in a finite set D={d1,…,dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K≥3, there exists a class of neither Pólya nor i.i.d. D-valued...

In various frameworks, to assess the joint distribution of a k-dimensional random vector X=(X1,…,Xk), one selects some putative conditional distributions Q1,…,Qk. Each Qi is regarded as a possible (or putative) conditional distribution for Xi given (X1,…,Xi−1,Xi+1,…,Xk). The Qi are...

Let a sequence of binary (zero–one or failure–success) trials ordered on a line. We consider runs of successes of length at least equal to a fixed number. The statistics denoting the size (length) as well as the starting and ending positions of the minimum subsequence containing all such...