Related papers: New generalized unit distributions based on order …
It is argued that polydispersed systems like colloids provide a direct example where Tsallis' statistical distribution is useful for describing the heirarchical nature of the system based on particle size.
We compare weighted sums of i.i.d. positive random variables according to the usual stochastic order. The main inequalities are derived using majorization techniques under certain log-concavity assumptions. Specifically, let $Y_i$ be i.i.d.…
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our…
The paper presents some distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts. Utilizing these properties, we extend several known results and obtain some new…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
We introduce and study the universal norm distribution in this paper, which generalizes the concepts of universal ordinary distribution and the universal Euler system. We study the Anderson type resolution of the universal norm distribution…
Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
Nowadays, huge amounts of data are naturally collected in distributed sites due to different facts and moving these data through the network for extracting useful knowledge is almost unfeasible for either technical reasons or policies.…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely-quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the…
We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical analysis…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly…
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to…