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Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
In this era of Big Data, proficient use of data mining is the key to capture useful information from any dataset. As numerous data mining techniques make use of information theory concepts, in this paper, we discuss how Fisher information…
Quark distribution and spectator functions are estimated in a diquark spectator model. The representation of the functions in terms of non-local operators together with the rather simple model allow estimates for the yet experimentally…
We conduct a review of the fiducial approach to statistical inference, following its journey from its initiation by R. A. Fisher, through various problems and criticisms, on to its general neglect, and then to its more recent resurgence.…
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In…
The geometric shapes of the outside world objects hide an undisclosed emotional, psychological, artistic, aesthetic and shape-generating potential; they may attract or cause fear as well as a variety of other emotions. This suggests that…
Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined perceptual scale. The perceptual scale can be…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending L\^e's theory in \cite{Le2020} to include weakly $C^k$-diffeological…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal composition of a function and a linear operator, and the…
In this paper, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…