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We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally,…

Computation · Statistics 2017-11-15 Nadhir Ben Rached , Zdravko Botev , Abla Kammoun , Mohamed-Slim Alouini , Raul Tempone

We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford functional calculus. Compared to related schemes, the new…

Numerical Analysis · Mathematics 2020-12-11 Alexander Rieder

This paper introduces chi-square goodness-of-fit tests to check for conditional distribution model specification. The data is cross-classified according to the Rosenblatt transform of the dependent variable and the explanatory variables,…

Econometrics · Economics 2023-09-25 Miguel A. Delgado , Julius Vainora

The classic chi-squared statistic for testing goodness-of-fit has long been a cornerstone of modern statistical practice. The statistic consists of a sum in which each summand involves division by the probability associated with the…

Computation · Statistics 2015-03-17 William Perkins , Mark Tygert , Rachel Ward

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

Numerical Analysis · Mathematics 2022-04-12 Kai Diethelm

We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set constructed relative to another cdf and, possibly, incorporating soft information. Our…

Optimization and Control · Mathematics 2024-08-23 Julio Deride , Johannes O. Royset , Fernanda Urrea

The recently developed "Data Set Diagonalization" method (DSD) is applied to measure compatibility of the data sets that are used to determine parton distribution functions (PDFs). Discrepancies among the experiments are found to be…

High Energy Physics - Phenomenology · Physics 2010-04-22 Jon Pumplin

In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…

Numerical Analysis · Mathematics 2021-11-17 Gustav Ludvigsson , Kyle R. Steffen , Simon Sticko , Siyang Wang , Qing Xia , Yekaterina Epshteyn , Gunilla Kreiss

I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find…

Astrophysics · Physics 2007-05-23 Luca Amendola

We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…

Numerical Analysis · Mathematics 2019-02-05 Andrea Bonito , Juan Pablo Borthagaray , Ricardo H. Nochetto , Enrique Otarola , Abner J. Salgado

In this correspondence, we point out two typographical errors in Chai and Tjhung's paper and we offer the correct formula of the unified Laguerre polynomial-series-based cumulative distribution function (cdf) for small-scale fading…

Probability · Mathematics 2011-02-10 Yin Sun , Arpad Baricz , Shidong Zhou

We develop a general method to quantify the uncertainties of parton distribution functions and their physical predictions, with emphasis on incorporating all relevant experimental constraints. The method uses the Hessian formalism to study…

High Energy Physics - Phenomenology · Physics 2008-12-18 J. Pumplin , D. Stump , R. Brock , D. Casey , J. Huston , J. Kalk , H. L. Lai , W. K. Tung

In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…

Methodology · Statistics 2016-07-11 A. Llera , C. F. Beckmann

Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence…

Probability · Mathematics 2020-12-22 Sergey G. Bobkov , Alexey A. Naumov , Vladimir V. Ulyanov

Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…

Numerical Analysis · Mathematics 2021-08-31 Sebastian Ament , Michael O'Neil

In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…

Methodology · Statistics 2023-12-29 Hong Zhang , Judong Shen , Zheyang Wu

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…

Machine Learning · Statistics 2024-07-31 Abhranil Das , Wilson S Geisler

Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…

Information Theory · Computer Science 2017-12-27 Dusan Jakovetic

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the…

Numerical Analysis · Mathematics 2016-05-12 A. Gil , J. Segura , N. M. Temme

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…

Machine Learning · Statistics 2024-06-27 Cencheng Shen , Sambit Panda , Joshua T. Vogelstein