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A bias analysis of Weibull models under heaped data by Augustin T., Wolff J.

By Augustin T., Wolff J.

Retrospectively amassed length information are frequently pronounced incorrectly. an enormous kind of such an mistakes is heaping - respondents are inclined to round-off or round-up the information based on a few rule of thumb. for 2 specific circumstances of the Weibull version we examine the behaviour of the 'naive estimators', which easily forget about the dimension blunders as a result of heaping, and derive closed expressions for the asymptotic bias. those effects provide a proper justification of empirical facts and simulation-based findings mentioned within the literature. also, events the place a notable bias should be anticipated might be pointed out, and an actual bias correction could be played.

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4] H. Kubinyi, Calculation of isotope distributions in mass spectrometry. A trivial solution for a non-trivial problem, Anal. Chim. Acta 1991, 247, 107. 8 ppm CH st CH3 δ as CH2 δ CH3 δ sy CH2 γ Fragments UV Lower shift values in three-membered rings 3000–2840 cm-1 Higher frequency in three-membered rings ≈1460 cm-1 ≈1460 cm-1 ≈1380 cm-1 Doublet for geminal methyl groups 770–720 cm-1 In C–(CH2)n–C with n ≥ 4 at ca. 0 Hz C n Long-range coupling, 4JHC–C=CH 0–2 Hz IR H–C(=C) st 3100–3000 cm-1 C=C st 1690–1635 cm-1 Of variable intensity H–C(=C) δ oop 1000–675 cm-1 CH2–(C=C) δ 1440 cm-1 MS Molecular ion Fragments m/z 14n m/z 14n - 2 m/z 14n - 1 m/z 14n - 3 Rearrangements Alkenes: moderate intensity Monocycloalkenes: medium intensity Local maxima for alkenes Local maxima for monocyclic alkenes Usually, double bonds cannot be localized n-Alkenes: unspecific except for: +.

M+9]+·) rather than 18 peaks, as they would be expected for very high resolution. Moreover, the contribution of isotopes of low abundance can often be neglected without sacrificing much precision. For example, the effect of 2H on isotope patterns is usually insignificant. Also, 13C is often negligible when focussing on peaks of the series [M+2n]+·, which then results in patterns that are characteristic for halogens, sulfur, and silicon. In large molecules, however, isotopes of low abundance cannot be neglected.

A 2003, 729, 337. K. R. de Laeter, P. De Bièvre, H. S. R. D. Taylor, Isotopic compositions of the elements, 2001, J. Phys. Chem. Ref. Data 2005, 34, 57. [4] H. Kubinyi, Calculation of isotope distributions in mass spectrometry. A trivial solution for a non-trivial problem, Anal. Chim. Acta 1991, 247, 107. 8 ppm CH st CH3 δ as CH2 δ CH3 δ sy CH2 γ Fragments UV Lower shift values in three-membered rings 3000–2840 cm-1 Higher frequency in three-membered rings ≈1460 cm-1 ≈1460 cm-1 ≈1380 cm-1 Doublet for geminal methyl groups 770–720 cm-1 In C–(CH2)n–C with n ≥ 4 at ca.

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