Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

La foi d'Israel, ses dogmes, son culte, ses cérémonies et pratiques religieuses, sa loi morale et sociale, sa mission et son avenir

par S. Bloch

Loi de Moise ou Système religieux et politique des Hébreux

par J. Salvador

L' esprit du judaisme ou examen raisonné de la loi moyse & de son influence sur la religion chrétienne

[Anthony Collins. Übers.[[Elektronische Ressource]] : Paul Heinrich Dietrich Frhr von Holbach]

Beilises protzes in Kiew : loiṭn sṭenografišen berichṭ ; in 3 ṭeilen

unṭer der redaktzie fun S. Biber

Sēfer Šabbat šabbātôn : 1. abṭheilung enṭhalṭ foršrifṭen loiṭ den geboṭen der toire ... di am šabbes tzu beobachṭen zind ...

ferfasṭ und heroisgegeben fon ... Šimʿôn Miller

ʿEzrâ has-sôfēr : loiṭ tanach, talmudim un midrošim

Jiśroel Šur

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.