Recently Tezuka introduced the concept of (u, e, s)-sequences which generalizes (t, s)-sequences by Niederreiter. This generalization can be used to point out a deeper regularity of certain digital sequences, which can be exploited to obtain improvements on their discrepancy bounds. Earlier Larcher and Niederreiter introduced so-called (T , s)-sequences with similar consequences. In this paper ...

In 1959 Chernoff [7] initiated the study of the asymptotic theory of sequential Bayes tests as the cost of observation tends to zero. He dealt with the case of a finite parameter space. The definitive generalization of the line of attack initiated in that paper was given by Kiefer and Sacks in [13]. Their work as well as that of Chernoff, the intervening papers of Albert [1], Bessler [3], and S...

We prove that a random choice rule satisfies Luce's Choice Axiom if and only its support is correspondence the Weak of Revealed Preference, thus it consists alternatives are optimal according to some preference, then occurs tie-breaking mechanism among such Renyi's Conditioning Axiom. Our result shows is, in precise formal sense, probabilistic version It supports view his own axiom as “canon ra...

We discuss five ways of proving Chernoff’s bound and show how they lead to different extensions of the basic bound.

We derive simple Chebyshev polynomial approximations for the density function and cumulative distribution function of the Chernoff distribution. They provide 6 significant figure accuracy with extreme efficiency.

-I4 ET US consider the usual decision-theory problem of classifying an observation X ss coming from one of m possible classes (hypotheses) C,, CZ, * , C,. Let nl, .a * , 7~,,, denote the a priori probabilities on the hypotheses, and let p,(x), * * * , p,(x) denote the conditional probability density functions given the true hypothesis. Let us assume that these are known. Then it is well knoti t...

We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both 2(δ) and 2δ fail, then δ is subcompact in a class inner model. If in addition 2(δ) fails, we prove that δ is Π21 subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. A...

Basu and Van (1998) present a fundamental framework of child labor with two important axioms: the luxury axiom and the substitution axiom. A number of empirical studies, however, reveal a “wealth paradox”. The current paper has two aims. First, it develops a model that provides an explanation for “the wealth paradox” in light of the luxury axiom and the substitution axiom. Second, it helps unde...

Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally impor...