Related papers: Scaling Exponent for Incremental Records

We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution rho. The running record equals the maximum of all elements in the sequence up…

In the context of this paper, a record is an entry in a sequence of random variables (RV's) that is larger or smaller than all previous entries. After a brief review of the classic theory of records, which is largely restricted to sequences…

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the…

We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a…

We study the statistics of increments in record values in a time series $\{x_0=0,x_1, x_2, \ldots, x_n\}$ generated by the positions of a random walk (discrete time, continuous space) of duration $n$ steps. For arbitrary jump length…

We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the…

We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width $p$ of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general…

Let $X_1, X_2,\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \geq 2.$ Let $X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1,…

Let $\boldsymbol{X}_1,\boldsymbol{X}_2,\dots$ be independent copies of a random vector $\boldsymbol{X}$ with values in $\mathbb{R}^d$ and with a continuous distribution function. The random vector $\boldsymbol{X}_n$ is a complete record, if…

We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the…

The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…

We characterize the exponential distribution in terms of the regression of a record value with non-adjacent record values as covariates. We also study characterizations based on the regression of linear combinations of record values.

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

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 $\Delta>0$. Rounding leads to ties of an existing record,…

Records among a sequence of iid random variables $X_1,X_2,\dotsc$ on the real line have been investigated extensively over the past decades. A record is defined as a random variable $X_n$ such that $X_n>\max(X_1,\dotsc,X_{n-1})$. Trying to…

We investigate the statistics of three kinds of records associated with planar random walks, namely diagonal, simultaneous and radial records. The mean numbers of these records grow as universal power laws of time, with respective exponents…

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…

Bairamov et al. (Aust N Z J Stat 47:543-547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of…

We investigate the probability of observing a given pattern of $n$ rises and falls in a random stationary data series. The data are modelled as a sequence of $n+1$ independent and identically distributed random numbers. This probabilistic…

We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very…