Related papers: Fractional exclusion statistics with incomplete in…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
The Generalized Fermi Breakup recently demonstrated to be formally equivalent to the Statistical Multifragmentation Model, if the contribution of excited states are included in the state densities of the former, is implemented. Since this…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual…
The attributable fraction among the exposed (\textbf{AF}$_e$), also known as the attributable risk or excess fraction among the exposed, is the proportion of disease cases among the exposed that could be avoided by eliminating the exposure.…
Data with missing values is ubiquitous in many applications. Recent years have witnessed increasing attention on prediction with only incomplete data consisting of observed features and a mask that indicates the missing pattern. Existing…
We consider the recent description of elementary particles in terms of Quantum Mechanical Kerr-Newman Black Holes, a description which provides a rationale for and at the same time reconciles the Bohm-hydrodynamical formulation on the one…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…
This paper sets a theoretical foundation for the applications of the fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements of the…
Federated Learning (FL) enables collaborative training across decentralized clients, but most methods assume aligned feature schemas, an assumption that rarely holds in tabular settings where clients observe only partially overlapping…
In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to…
When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new asymptotic theory about inference with missing data that is more general than…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
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…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
We introduce the notion of `order-$k$ non-abelian exclusion statistics'. We derive the associated thermodynamic equations by employing the Thermodynamic Bethe Ansatz for specific non-diagonal scattering matrices. We make contact with…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the…