Related papers: Distributional Point Values and Delta Sequences
In this paper, we revisit pattern mining and study the distribution underlying a binary dataset thanks to the closure structure which is based on passkeys, i.e., minimum generators in equivalence classes robust to noise. We introduce…
The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby…
For an arbitrary complex number $a\neq 0$ we consider the distribution of values of the Riemann zeta-function $\zeta$ at the $a$-points of the function $\Delta$ which appears in the functional equation $\zeta(s)=\Delta(s)\zeta(1-s)$. These…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating…
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…
The notion of pointwise differentials for distributions is a way to extract local information of distributions by rescaling the distribution at a point. In this paper, we study the pointwise differentials for distributions corresponding to…
A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal,…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
We compute the limiting distribution, as n approaches infinity, of the number of cycles of length between gamma n and delta n in a permutation of [n] chosen uniformly at random, for constants gamma, delta such that 1/(k+1) <= gamma < delta…
This paper generalizes the traditional statistical concept of prediction intervals for arbitrary probability density functions in high-dimensional feature spaces by introducing significance level distributions, which provides…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of…
For a generalized scale function of standard processes, we characterize it as a unique solution to a Volterra type integral equation. This allows us to extend it to an entire function and to derive a useful identity that we call the…
For various plasma applications the so-called (non-relativistic) $\kappa$-distribution is widely used to reproduce and interpret the suprathermal particle populations exhibiting a power-law distribution in velocity or energy. Despite its…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…