34,301 research outputs found

    On approximation of Markov binomial distributions

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    For a Markov chain X={Xi,i=1,2,...,n}\mathbf{X}=\{X_i,i=1,2,...,n\} with the state space {0,1}\{0,1\}, the random variable S:=i=1nXiS:=\sum_{i=1}^nX_i is said to follow a Markov binomial distribution. The exact distribution of SS, denoted LS\mathcal{L}S, is very computationally intensive for large nn (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for LS\mathcal{L}S when X\mathbf{X} is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for LS\mathcal{L}S when VarS\operatorname {Var}S is greater than and less than ES\mathbb{E}S, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ194 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Four Facets of Privacy and Intellectual Freedom in Licensing Contracts for Electronic Journals

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    This is a study of the treatment of library patron privacy in licenses for electronic journals in academic libraries. We begin by distinguishing four facets of privacy and intellectual freedom based on the LIS and philosophical literature. Next, we perform a content analysis of 42 license agreements for electronic journals, focusing on terms for enforcing authorized use and collection and sharing of user data. We compare our findings to model licenses, to recommendations proposed in a recent treatise on licenses, and to our account of the four facets of intellectual freedom. We find important conflicts with each

    Atmospheric Charged K/πK/\pi Ratio and Measurement of Muon Annual Modulation with a Liquid Scintillation Detector at Soudan

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    We report a measurement of muon annual modulation in a 12-liter liquid scintillation detector with a live-time of more than 4 years at the Soudan Underground Laboratory. Muon minimum ionization in the detector is identified by its observed pulse shape and large energy deposition. The measured muon rate in the detector is 28.69±\pm2.09 muons per day with a modulation amplitude of 2.66±\pm 1.0\% and a phase at Jul 22 ±\pm 36.2 days. This annual modulation is correlated with the variation of the effective atmospheric temperature in the stratosphere. The correlation coefficient, αT\alpha_{T}, is determined to be 0.898±0.0250.898 \pm 0.025. This can be interpreted as a measurement of the atmospheric charged kaon to pion (KK/π\pi) ratio of 0.0940.061+0.044^{+0.044}_{-0.061} for Ep>E_{p} > 7 TeV, consistent with the measurement from the MINOS far detector. To further constrain the value of KK/π\pi ratio, a Geant4 simulation of the primary cosmic-ray protons with energy up to 100 TeV is implemented to study the correlation of KK/π\pi ratio and the muon annual modulation for muon energy greater than 0.5 TeV. We find out that a charged KK/π\pi ratio of 0.1598, greater than the upper bound (0.138) from this work at the production point 30 km above the Earth surface in the stratosphere cannot induce muon annual modulation at the depth of Soudan.Comment: 6 pages and 11 figure