arXiv subjects

G. Wergen

Publications and source records attributed to G. Wergen.

2 recordsLinked to original sources

arXiv2012

Rounding Effects in Record Statistics

We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding down to integer multiples of a discretization scale $Δ>0$. Rounding leads to ties of an existing record, thereby reducing the number of new records. For an infinite number of random variables that are drawn from distributions with a finite upper limit, the number of discrete records is finite, while for distributions with a thinner than exponential upper tail, fewer discrete records arise compared to continuous variables. In the latter case the record sequence becomes highly regular at long times.

physics.data-an↗

arXiv2012

Correlations of record events as a test for heavy-tailed distributions

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively (negatively) correlated when the tail of the distribution is heavier (lighter) than exponential. Here we use these correlations to detect heavy-tailed behavior in small sets of independent random variables. The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations.

physics.data-an↗