The chi-squared test of Markov chain lumpability is shown to operate reliably under a corrected derivation of the degrees of freedom. The test is used to screen out lumping schemes that corrupt the Markov property and give rise to higher order dependence

Based on a non-parametric criterion of independence derived from a generalized version of the Schweizer-Wolff non-parametric measure of dependence, we calculate rates of convergence to asymptotic independence between the order statistics in a general setting. Three different rates of convergence...

The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density f(x)~f_0 x^(-2), with the coefficient depending on the means and variances of the numerator and denominator, and their correlation. We also obtain the conditional...

Ramsey's failure to grasp the interval valued and non additive nature of Keynesian probability assessments in the A Treatise on Probability has led to the misbelief that Keynes's approach was an ordinal one. While Keynes's approach easily handles ordinal probability, the theory of the Treatise...

We prove Khinchin's Theorems for Gelfand pairs (, ) satisfying a condition (*): (a) is connected; (b) is almost connected and Ad (/) is almost algebraic for some compact normal subgroup ; (c) admits a compact open normal subgroup; (d) (, ) is symmetric and is 2-root compact; (e) is a...

The class of bivariate extreme value copulas, which satisfies the monotone regression positive dependence property or equivalently the stochastic increasing property, is considered. A variational calculus proof of the Hutchinson-Lai conjecture about Kendall's tau and Spearman's rho for this...

and subtracting the product from 1.0, the mutual support of semantically independent conjuncts is quantified. While for the Bayesian method, three empirical data are prerequisite, two such data may suffice for the "MPE-Method"

This paper introduces a general technique for estimating the absolute value of the exponential sum for all composite integers k ≠ , a prime power. The new estimate improves the classical estimate by a factor of about 2 or better (depending on ) for all sufficiently large primes Further, it...

Given a Markov operator on a -finite measure space (, Σ, ) and is invariant, we say that has Krengel-Lin decomposition if () = ⊕ (, Σ) where = { ∈ () | ‖()‖ → 0} and Σ is the deterministic -field of . We consider the case of convolution operator and we show that a measure λ on a...

Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around the line of integration in the complex plane.The Fourier transform techniques reduces calculation of probability distributions and option...