Because these fields are closely related, and since this relation is not yet a common knowledge, I would like it to be known to the interval community. Yes, terms that we use are different, and mathematical methods are different, but these different methods are used to solve the same application problems. In solving these problems, interval and maximum entropy methods not only do not compete, t...

We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterizati...

An approach to the Shannon and Rényi entropy maximization problems with constraints on the mean and law invariant deviation measure for a random variable has been developed. The approach is based on the representation of law invariant deviation measures through corresponding convex compact sets of nonnegative concave functions. A solution to the problem has been shown to have an alpha-concave d...

where ci is the D-dimensional vector of the ith link, and i ­ 1, . . . , b. The right-hand side of Eq. (1) is the LBGK collision integral Di , the function N eq i is the local equilibrium, and v $ 0 is a dimensionless parameter. As the state of the lattice is updated long enough, the dynamics of Ni becomes governed by macroscopic equations for a finite system of local averages. Depending on the...

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We appl...

Recently we used the maximum entropy principle for finding the price density in a multi agent insurance market. The result is similar to what the Buhlmann had obtained by maximizing the utility function. Here we begin with the price density that is derived by applying the maximum entropy principle to a conservative economic system (exchange market), then reverse the Buhlmann calculation to find...

In this paper we consider the maximum entropy principle with imprecise side-conditions, where the imprecise side-conditions are modeled as fuzzy sets. Our solution produces fuzzy discrete probability distributions and fuzzy probability density functions.

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief functi...