Related papers: An exactly solvable record model for rainfall
In this work the information loss in deterministic, memoryless systems is investigated by evaluating the conditional entropy of the input random variable given the output random variable. It is shown that for a large class of systems the…
This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data---which results from the dimension,…
Predicting future states or actions of a given system remains a fundamental, yet unsolved challenge of intelligence, especially in the scope of complex and non-deterministic scenarios, such as modeling behavior of humans. Existing…
We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus…
Abundance data are used in ecology for species monitoring and conservation. These count data often display several specific characteristics like numerous missing data, high variance, and a high proportion of zeros, particularly when…
Given key performance indicators collected with fine granularity as time series, our aim is to predict and explain failures in storage environments. Although explainable predictive modeling based on spiky telemetry data is key in many…
In this paper we study records obtained from partial comparisons within a sequence of independent and identically distributed (i.i.d.) random variables, indexed by positive integers, with a common density~\(f.\) Our main result is that if…
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…
This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics,…
We compute exactly the mean number of records $\langle R_N \rangle$ for a time-series of size $N$ whose entries represent the positions of a discrete time random walker on the line. At each time step, the walker jumps by a length $\eta$…
What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
We study the occurrence of events, subject to threshold, in a representative SOC sandpile model and in high-resolution rainfall data. The predictability in both systems is analyzed by means of a decision variable sensitive to event…
In this paper we consider the two-type Moran model with $N$ individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution ${\mathbb P}$ on ${\mathbb R}_+$, and a type, either $1$ or $0$.…
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 use the statistical properties of Shannon entropy estimator and Kullback-Leibler divergence to study the predictability of ultra-high frequency financial data. We develop a statistical test for the predictability of a sequence based on…
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary…
The modelling of the occurrence of rainfall dry and wet spells (ds and ws, respectively) can be jointly conveyed using the inter-arrival times (it). While the modelling of it has the advantage of requiring a single fitting for the…
Calibration of hydrological time-series models is a challenging task since these models give a wide spectrum of output series and calibration procedures require significant amount of time. From a statistical standpoint, this model parameter…