Related papers: Records in a changing world
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…
Turbulence is a complex spatial and temporal structure created by the strong non-linear dynamics of fluid flows at high Reynolds numbers. Despite being an ubiquitous phenomenon that has been studied for centuries, a full understanding of…
We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics…
We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…
Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher ($>$ two) order correlations, they offer a better measure…
This paper deals with Bayesian estimations of scale parameter of the exponential distribution based on upper record range (Rn). This has been done in two steps; point and interval. In the first step the quadratic, squared error and absolute…
Learning is a distinctive feature of intelligent behaviour. High-throughput experimental data and Big Data promise to open new windows on complex systems such as cells, the brain or our societies. Yet, the puzzling success of Artificial…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…
This study aims to introduce a new lifetime distribution, called the record-based transformed log-logistic distribution, to the literature. We obtain this distribution using a record-based transformation map based on the distributions of…
A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered…
Traditional statistics forbids use of test data (a.k.a. holdout data) during training. Dwork et al. 2015 pointed out that current practices in machine learning, whereby researchers build upon each other's models, copying hyperparameters and…
In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
The behavior of the leading singular values and vectors of noisy low-rank matrices is fundamental to many statistical and scientific problems. Theoretical understanding currently derives from asymptotic analysis under one of two regimes:…
The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency…
The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the 24 possible orders.…
We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$.…