Related papers: On sampling and parametrization of discrete freque…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study…
When data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to the set of measured values is a long debated problem. Given the data, the fitting would require to find which measurand value is most…
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…
The relation between the expectation values computed in the random walk theory, and the heat kernel method for the diffusion equation is explained concretely. The random walk is also realized by simulations and their statistical…
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…
We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the ob served values, we propose a different estimate, the high-profile…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies.…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.