Related papers: Elliptical Tempered Stable Distribution and Fracti…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
The relation between tempered distributions and measures is analysed and clarified. While this is straightforward for positive measures, it is surprisingly subtle for signed or complex measures.
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distributions. Our results suggest that these are…
We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that,…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
In the stochastic frontier model, the composed error term consists of the measurement error and the inefficiency term. A general assumption is that the inefficiency term follows a truncated normal or exponential distribution. In a wide…
Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…
We develop the first exact and computationally tractable method for simulating from tempered stable distributions in the infinite variation case, which corresponds to $\alpha\in[1,2)$. A small simulation study shows that the approach works…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…
In this paper we delve into some important properties of probability distributions of the power type in order to provide some answers to questions recently raised in the literature. More precisely, we focus on the properties of maximizers…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…