skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Binomial test statistics using Psi functions

Abstract

For the negative binomial model (probability generating function (p + 1 - pt){sup -k}) a logarithmic derivative is the Psi function difference {psi}(k + x) - {psi}(k); this and its derivatives lead to a test statistic to decide on the validity of a specified model. The test statistic uses a data base so there exists a comparison available between theory and application. Note that the test function is not dominated by outliers. Applications to (i) Fisher's tick data, (ii) accidents data, (iii) Weldon's dice data are included.

Authors:
 [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
Work for Others (WFO)
OSTI Identifier:
932030
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Far East Journal of Theoretical Statistics; Journal Volume: 23; Journal Issue: 1
Country of Publication:
United States
Language:
English
Subject:
97; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PROBABILITY; STATISTICS; MATHEMATICAL MODELS; CALCULATION METHODS; USES

Citation Formats

Bowman, Kimiko o. Binomial test statistics using Psi functions. United States: N. p., 2007. Web.
Bowman, Kimiko o. Binomial test statistics using Psi functions. United States.
Bowman, Kimiko o. Mon . "Binomial test statistics using Psi functions". United States. doi:.
@article{osti_932030,
title = {Binomial test statistics using Psi functions},
author = {Bowman, Kimiko o},
abstractNote = {For the negative binomial model (probability generating function (p + 1 - pt){sup -k}) a logarithmic derivative is the Psi function difference {psi}(k + x) - {psi}(k); this and its derivatives lead to a test statistic to decide on the validity of a specified model. The test statistic uses a data base so there exists a comparison available between theory and application. Note that the test function is not dominated by outliers. Applications to (i) Fisher's tick data, (ii) accidents data, (iii) Weldon's dice data are included.},
doi = {},
journal = {Far East Journal of Theoretical Statistics},
number = 1,
volume = 23,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • It is pointed out that the statistical component of the total error in activation analysis is in all practical cases subject to the Poisson distribution. (auth)
  • We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total ofmore » $$\Nprops$$ sets of measurements are made using $$\Ncfgs$$ gauge configurations of size $$20^3\times 128$$ with an anisotropy parameter $$\xi= b_s/b_t = 3.5$$, a spatial lattice spacing of $$b_s=0.1227\pm 0.0008~{\rm fm}$$, and pion mass of $$\mpi\sim 390~{\rm MeV}$$. Ground state baryons masses are extracted with fully quantified uncertainties that are at or below the $$\sim 0.2\%$$-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the $$N\pi$$ threshold and, therefore, the isos« less
  • We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292, 500 sets of measurements are made using 1194 gauge configurations of size 20{sup 3} x 128 with an anisotropy parameter {zeta} = b{sub s}/b{sub t} = 3.5, a spatial lattice spacing of b{sub s} = 0.1227 {+-} 0.0008 fm, and pion mass of M{sub {pi}} {approx} 390 MeV. Ground state baryons masses are extracted with fully quantifiedmore » uncertainties that are at or below the {approx} 0.2%-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the N{pi} threshold and, therefore, the isospin-1/2 {pi}N s-wave scattering phase-shift can be extracted using Luescher's method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time-slices. This is due to backward propagating states arising from the anti-periodic boundary conditions imposed on the quark-propagators in the time-direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables.« less