The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function φ(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann-Gibbs form with the exponential function replaced by a deformed exponential fun...

We show that auctions can generate near optimal total expected revenue by not using optimal reserve prices. Suppose we have n = 1 bidders in a posted-price, sealed-bid auction. This bidder has type v i drawn from distribution F. We can describe what the expected revenue is with a functionˆR : T → R: ˆ R(p) = p(1 − F(p)). (1) Figures 1 and 2 show expected revenue functions for the exponential di...

Gap-acceptance capacity models apply to the analysis of minor movements at two-way stop and give-way (yield) sign-controlled intersections, entry streams at roundabouts and opposed (permitted) turns at signalised intersections. The same modelling principles apply to all these cases with different model parameters representing the intersection geometry, control and driver behaviour at different ...

Epidemic models usually rely on the assumption of exponentially distributed sojourn times in infectious states. This is sometimes an acceptable approximation, but it is generally not realistic and it may influence the epidemic dynamics as it has already been shown in one population. Here, we explore the consequences of choosing constant or gamma-distributed infectious periods in a metapopulatio...

A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after s...