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Extremal Distributions of Discrepancy functions [article]

Ralph Kritzinger, Markus Passenbrunner
2019 arXiv   pre-print
We show a stronger result on the distribution of discrepancy functions of point sets in [0,1], which basically says that the distribution of the discrepancy function of Γ_N is in some sense minimal among  ...  The irregularities of a distribution of N points in the unit interval are often measured with various notions of discrepancy.  ...  The distribution of the one-parameter discrepancy function The function D and its extremal distribution are easily analyzed.  ... 
arXiv:1902.09877v2 fatcat:fdpyjs3vs5dtjhjg4yshe3ooxu

Statistical Inference of Gaussian-Laplace Distribution for Person Verification

Zheng Wang, Ruimin Hu, Yi Yu, Junjun Jiang, Jiayi Ma, Shin'ichi Satoh
2017 Proceedings of the 2017 ACM on Multimedia Conference - MM '17  
However, we find that, in fact, the distribution of discrepancies of positive pairs might tend to the Laplace distribution rather than the Gaussian distribution.  ...  Based on this finding, we propose a metric learning method by exploiting Gaussian-Laplace distribution statistical inference, where the Gaussian distribution of negative discrepancies and the Laplace distribution  ...  Program of China (2015AA016306).  ... 
doi:10.1145/3123266.3123421 dblp:conf/mm/WangHYJMS17 fatcat:djg24tmxdbazvaopcjw6j44jrm

Gaussian limits for discrepancies

André van Hameren, Ronald Kleiss, Jiri Hoogland
1998 Nuclear Physics B - Proceedings Supplements  
We investigated the asymptotic behaviour, in the limit of a. large number of points, of probability distributions of these discrepancies, a.nd were a.ble to formulate a.  ...  For a ma.thexna.tical analysis of these point sets measures of non-uniformity a.re needed. These measures a.re called discrepancies.  ...  Especially for the extreme discrepancy, many rigorous statements can be made [2) .  ... 
doi:10.1016/s0920-5632(97)00964-x fatcat:o5mwtbyy7ras5d5g6jralc63m4

Recent Progress in Improvement of Extreme Discrepancy and Star Discrepancy of One-Dimensional Sequences [chapter]

Victor Ostromoukhov
2009 Monte Carlo and Quasi-Monte Carlo Methods 2008  
In this communication, we report on recent progress in improvement of extreme discrepancy and star discrepancy of one-dimensional sequences.  ...  base 84, which improves the best known results for extreme discrepancy obtained by Henri Faure in 1992 [6].  ...  Among different metrics for evaluation of the uniformity of distributions, star discrepancy and extreme discrepancy play a special role.  ... 
doi:10.1007/978-3-642-04107-5_36 fatcat:lpqwiykunjguxpxwfzk3nzvqm4

Effects of Somatic Dysfunction on Leg Length and Weight Bearing

Yasmi Qureshi, Andrew Kusienski, Julienne Bemski, John Luksch, Lacy Knowles
2014 The Journal of the American Osteopathic Association  
Weight-bearing distribution through each lower extremity was measured on a quadruped scale. Participants were then evaluated for somatic dysfunctions of the pelvis, sacrum, and lower lumbar spine.  ...  Their association with leg length discrepancies has been observed; however, it is unclear which dysfunctions lead to mild changes in leg length or weight bearing distribution in asymptomatic individuals  ...  of data; Ms Qureshi, Dr Kusienski, and Student Doctor Bemski drafted the article or revised it critically for important intellectual content; and Ms Qureshi gave final approval of the version of the article  ... 
doi:10.7556/jaoa.2014.127 pmid:25082970 fatcat:skapfiyemrad7j5n5cgjgrqcde

Posterior Predictive Model Checking for Conjunctive Multidimensionality in Item Response Theory

Roy Levy
2011 Journal of educational and behavioral statistics  
Key findings include (a) support for the hypothesized effects of the manipulated factors and (b) the superiority of certain discrepancy measures for conducting posterior predictive model checking for dimensionality  ...  If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold.  ...  Discrepancy Measures Three univariate functions are evaluated at the item level and eight bivariate functions are evaluated for pairs of items.  ... 
doi:10.3102/1076998611410213 fatcat:6zbo2byilvgexhprq6bwalsp4a

Page 2376 of American Society of Civil Engineers. Collected Journals Vol. 114, Issue 10 [page]

1988 American Society of Civil Engineers. Collected Journals  
Extreme Type I Distribution Inches of Water Extreme Type I1 Distribution Analytical Distribution -98 .99.995 .998 .999 Cumulative Distribution Function FIG. 1.  ...  Comparison of Analytical and Extremal Cumulative Distribution Functions for Cleveland, Ohio oie) etal] where I'(.) = the gamma function.  ... 

Page 356 of Journal of Personality Vol. 27, Issue 3 [page]

1959 Journal of Personality  
, (6) decrease as the discrepancy between communicator and communi- catee increases, and (c) decrease more rapidly as a function of in- creasing discrepancy size for statements of opinion than for state  ...  Communications advocat- ing moderate and extreme positions on each side of each of these issues were prepared.  ... 

ABC model selection for spatial extremes models applied to South Australian maximum temperature data

Xing Ju Lee, Markus Hainy, James P. McKeone, Christopher C. Drovandi, Anthony N. Pettitt
2018 Computational Statistics & Data Analysis  
ABC algorithms rely on the evaluation of discrepancies between model simulations and the observed data rather than explicit evaluations of computationally expensive or intractable likelihood functions.  ...  Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory.  ...  We only require the discrepancy function to induce an ordering of the simulated data with respect to the observed data.  ... 
doi:10.1016/j.csda.2018.06.019 fatcat:miuepq3zmrd7xksrlxlgwoc7yq

Combining Groundwater Flow Modeling and Local Estimates of Extreme Groundwater Levels to Predict the Groundwater Surface with a Return Period of 100 Years

Hans Kupfersberger, Gerhard Rock, Johannes C. Draxler
2020 Geosciences  
Typically, distributions of extreme groundwater levels are generated by interpolation between results derived from local extreme value analysis at groundwater observation wells.  ...  We demonstrate the applicability of the approach at the Südliches Wiener Becken (SWB) aquifer south of Vienna, where a groundwater flow model between 1993 to 2017 is available to compute the distribution  ...  Acknowledgments: We kindly acknowledge the permission of the water resources management division of the Federal Government of Lower Austria to use the groundwater model of the Südliches Wiener Becken.  ... 
doi:10.3390/geosciences10090373 fatcat:qczblbmkgbgfnonxkmdgv4pyfy

A New Calibrated Bayesian Internal Goodness-of-Fit Method: Sampled Posterior p-Values as Simple and General p-Values That Allow Double Use of the Data

Frédéric Gosselin, Pedro Antonio Valdes-Sosa
2011 PLoS ONE  
As a result, no known GOF p-value has a known probability distribution for any discrepancy function.  ...  Recent approaches mixing frequentist principles with Bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of Bayesian statistical models.  ...  Acknowledgments The author thanks Elfie Perdereau for discussion on the posterior predictive checks, Vicki Moore for correcting the English, and Claude Millier and Marion Gosselin for re-reading a previous version of  ... 
doi:10.1371/journal.pone.0014770 pmid:21445246 pmcid:PMC3060804 fatcat:rpmlvo3grjchza4gvhhyd5vrle

Contrast trees and distribution boosting

Jerome H. Friedman
2020 Proceedings of the National Academy of Sciences of the United States of America  
Contrast trees provide a lack-of-fit measure for statistical models of such statistics, or for the complete conditional distribution py(y | x), as a function of x.  ...  z | x, or selected properties of those distributions such as means or quantiles, are most different.  ...  Important discussions with Trevor Hastie and Rob Tibshirani on the subject of this work are gratefully acknowledged.  ... 
doi:10.1073/pnas.1921562117 pmid:32817416 fatcat:rj7uyhl6zrbwbj5w7irbh6qwja

11th International Conference on Conservative Management of Spinal Deformities - SOSORT

2014 Scoliosis  
In the first study, a functional shortening of the left lower extremity predominated in the girls, while in the second study it was the right lower extremity and was identified in the boys.  ...  The exam consisted of: (1) clinical assessment of pelvic symmetry, (2) functional lower limb discrepancy assessment based on Rippstein plurimeter measurement of iliac spines position.  ... 
pmid:25932620 pmcid:PMC4290216 fatcat:vxj4gmumgzg5nf26dyviiprbyi

THE IMPACT OF LOWER LIMB-LENGTH EQUALISATION ON POSTURAL STABILITY IN PATIENTS TREATED WITH THE ILIZAROV METHOD

Łukasz Pawik, Piotr Morasiewicz, Zdzisława Wrzosek, Felicja Fink-Lwow, Malwina Pawik
2019 Journal of Men's Health  
to a control group, which consisted of people with lower extremities of equal lengths.  ...  The measurement was made using the Biodex Balance System, which enables examination of the patient's ability to control balance and to assess the patient's lower-limb support function by determining their  ...  Balance and symmetrical load distributions between both lower extremities influence the biomechanics of the musculoskeletal system.  ... 
doi:10.22374/jomh.v15i3.149 doaj:67c26d7fa44143fbbcb7efe55a47f0a2 fatcat:vqrwcee4a5gbhi54wb7o2lh6my

Uniformly distributed sequences generated by a greedy minimization of the L_2 discrepancy [article]

Ralph Kritzinger
2022 arXiv   pre-print
The approach we follow here is motivated by recent work of Steinerberger and Pausinger who consider similar greedy algorithms, where they minimize functionals that can be related to the star discrepancy  ...  The figures of merit are three different variants of L_2 discrepancy. Theoretical results along with numerical experiments suggest that the resulting sequences have excellent distribution properties.  ...  Acknowledgements I would like to thank Stefan Steinerberger for his friendly feedback and his suggestions on how to highlight the most interesting aspects of the results more clearly.  ... 
arXiv:2109.06298v4 fatcat:tb3d53yrbngcfnp7mzpt5uknde
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