相关论文: Records in a changing world
In this paper, we investigate inaccuracy measures based on record values, focusing on the relationship between the distribution of the n-th upper and lower k-record values and the parent distribution. We extend the classical Kerridge…
How long is needed for an observable to exceed its previous highest value and establish a new record? This time, known as the age of a record plays a crucial role in quantifying record statistics. Until now, general methods for determining…
We address the question of distance record-setting by a random walker in the presence of measurement error, $\delta$, and additive noise, $\gamma$ and show that the mean number of (upper) records up to $n$ steps still grows universally as…
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the…
We investigate conditions in order to decide whether a given sequence of real numbers represents expected record values arising from an independent, identically distributed, sequence of random variables. The main result provides a necessary…
World record setting has long attracted public interest and scientific investigation. Extremal records summarize the limits of the space explored by a process, and the historical progression of a record sheds light on the underlying…
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements…
The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations…
Let $X_i,i=0,1,\ldots$ be a sequence of iid random variables whose distribution is continuous. Associated with this sequence is the sequence $(i,X_i),i=0,1,\ldots$. Let ${\cal R}_{n}$ denote the set of Pareto optimal elements of $\{…
We write $R_n$ for the minimal position attained after time $n$ by a branching random walk in the boundary case. In this article, we prove that $R_n - \frac{1}{2} \log n$ converges in law toward a shifted Gumbel distribution.
We study the record statistics of random walks after $n$ steps, $x_0, x_1,\ldots, x_n$, with arbitrary symmetric and continuous distribution $p(\eta)$ of the jumps $\eta_i = x_i - x_{i-1}$. We consider the age of the records, i.e. the time…
We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we…
In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
Let $q>r\ge1$ be coprime integers. Let $R(n,q,r)$ be the $n$th record gap between primes in the arithmetic progression $r$, $r+q$, $r+2q,\ldots,$ and denote by $N_{q,r}(x)$ the number of such records observed below $x$. For $x\to\infty$, we…
Permanents of random matrices with independent and identically distributed (i.i.d.) entries have extensively studied in literature and convergence and concentration properties are known under varying assumptions on the distributions. In…
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…