Given an i.i.d. sequence of n letters from a finite alphabet, we consider the length of the longest run of any letter. In the equiprobable case, results for this run turn out to be closely related to the well-known results for the longest run of a given letter. For coin-tossing, tail probabilities are compared for both kinds of runs via Poisson approximation.

We present recent results about the long-run average properties of probabilistic vector additions systems with states (pVASS). Interestingly, for probabilistic pVASS with two or more counters, long-run average properties may take several different values with positive probability even if the underlying state space is strongly connected. This contradics the previous results about stochastic Petr...

Previous research has shown that many choice biases are attenuated when short-run decisions are reframed to the long run. However, this literature has been limited to description-based choice tasks in which possible outcomes and their probabilities are explicitly specified. A recent literature has emerged showing that many core results found using the description paradigm do not generalize to e...

The run statistics of a discrete-time, real-valued stochastic process are the statistics of process excursions above a given level. As such they are a special case of first passage times (hitting times) in discrete time. The study of run probabilities is motivated by applications such as compressed video, where a random and autocorrelated sequence of compressed frames arrives deterministically ...

abstract the present research accomplished to determination of the trade liberalization effects on import function of iran’s wheat crop using time series data from 1357 to 1387 that earn from sources such as agricultural and aerology statistics annual letter, customhouse and iran central bank website.in this investigation, at first, wheat liberalization index was measured by using level of inte...

Consider a finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the Ž . correct but unknown probabilities. The forecast is calibrated if observed ...