Related papers: A note on tempered measures
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
We characterize the distributions that arise as derivatives of families of probabilities and of positive and signed measures on smooth manifolds.
A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
These informal notes are concerned with sums and averages in various situations in analysis.
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
The presence of latent variables can greatly complicate inferences about causal relations between measured variables from statistical data. In many cases, the presence of latent variables makes it impossible to determine for two measured…
As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
The aim of this research is to give a simple framework to evaluate/quantize the "transparency" of a firm. We assume that the process of the firm value is only observable once in a while but is strongly correlated with the stock price which…
Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned…
We study the relationship between different kinds of convergence of finite signed measures and discuss their metrizability. In particular, we study the concept of basic convergence recently introduced by Khartov [arXiv:2204.13667] and…
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…