Least Median of Squares (LMS) and Least Trimmed Squares (LTS) Fitting for the Weighted Arithmetic Mean

2018 ◽  
pp. 367-378 ◽  
Author(s):  
Gleb Beliakov ◽  
Marek Gagolewski ◽  
Simon James
Keyword(s):  
Arithmetic Mean ◽  
Least Trimmed Squares ◽  
Weighted Arithmetic ◽  
Least Median Of Squares

scholarly journals The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 380 ◽  
Author(s):  
Yongtao Li ◽  
Xian-Ming Gu ◽  
Jianxing Zhao
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Hölder Inequality ◽  
Power Mean ◽  
Weighted Arithmetic ◽  
Mathematical Equivalence ◽  
Power Mean Inequality ◽  
Mathematical Relations

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

Geospatial Suitability Indices Toolbox (GSI Toolbox)

2021 ◽  
Author(s):  
Christina Saltus ◽  
Todd Swannack ◽  
S. McKay
Keyword(s):  
Habitat Suitability ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Limiting Factor ◽  
Ecological Processes ◽  
Weighted Arithmetic ◽  
Suitability Index ◽  
Multiple Parameter ◽  
Spatially Distributed

Habitat suitability models are widely adopted in ecosystem management and restoration, where these index models are used to assess environmental impacts and benefits based on the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). Here, we present a geospatial toolbox for assessing habitat suitability. The Geospatial Suitability Indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python® 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the Suitability Index Calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices based on user-specified habitat relationships. Second, the Overall Suitability Index Calculator combines multiple parameter suitability indices into one overarching index using one or more options, including: arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The resultant output is a raster layer representing habitat suitability values from 0.0 to 1.0, where zero is unsuitable habitat and one is ideal suitability. This report documents the model purpose and development as well as provides a user’s guide for the GSI toolbox.

Inter-laboratory calibration of a Ag3PO4 comparison material for oxygen stable isotope analysis

2020 ◽  
Author(s):  
Andrea Watzinger ◽  
Katharina Schott ◽  
Rebecca Hood-Nowotny ◽  
Grzegorz Skrzypek ◽  
Federica Tamburini ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
High Temperature ◽  
Stable Isotope ◽  
Natural Resources ◽  
Life Science ◽  
Arithmetic Mean ◽  
Environmental Research ◽  
Weighted Arithmetic ◽  
Laboratory Calibration ◽  
The University

<p>A silver phosphate comparison material (Ag<sub>3</sub>PO<sub>4</sub>) for measurement of the stable oxygen isotope composition was prepared by the University of Natural Resources and Life Science (BOKU) and distributed to four international isotope laboratories frequently measuring the δ<sup>18</sup>O value in Ag<sub>3</sub>PO<sub>4</sub>. The contributing laboratories were the University of Natural Resources and Life Science (BOKU), The University of Western Australia (UWA), the ETH Zurich (ETH), the University of Helsinki (UH) and the Helmholtz Centre for Environmental Research (UFZ). Each laboratory analysed the comparison material in a minimum of two independent measuring rounds with a minimum of 10 individual measurements. The instrument used to perform the measurements were high-temperature conversion elemental analyzers coupled with continuous flow isotope ratio mass spectrometers: TC/EA with Thermo Finnigan Delta XP (BOKU), a TC/EA with a Thermo Scientific Delta V Plus (UWA), an Elementar Pyrocube with a Isoprime 100 (ETH), a Flash IRMS EA with a Thermo Scientific Delta V Plus (UH) and a TC/EA with a Finnigan Delta S (UFZ). The working gas δ<sup>18</sup>O was set to 0 ‰ and the normalization was done by a three-point linear regression calibration (Paul et al., 2007) using the reference material IAEA-601 (δ<sup>18</sup>O<sub>VSMOW</sub> = +23.14 ± 0.17 ‰), IAEA-602 (δ<sup>18</sup>O<sub>VSMOW</sub> = +71.28 ±0.42 ‰) (both benzoic acid) and NBS 127 (barium sulfate) (δ<sup>18</sup>O<sub>VSMOW</sub> = +8.59 ± 0.20 ‰) (Brand et al., 2009). BOKU, UH and ETH had experienced inhomogeneity of the IAEA-602 as already mentioned in Brand et al. (2009). The weighted arithmetic mean and standard deviation (1σ) of the new BOKU Ag<sub>3</sub>PO<sub>4</sub> comparison material from the single measurements has a δ<sup>18</sup>O value of 13.80 ± 0.40 ‰ on the VSMOW scale (n=131), while the median of the single rounds was 13.76 ‰ (n=11) and the median of the laboratories was 13.79 ‰ (n=5). The arithmetic means of two measuring rounds were outside ± 1σ. When excluding data from these rounds from the statistics the weighted arithmetic mean has a δ<sup>18</sup>O value of 13.80 ± 0.32 ‰ on the VSMOW scale (n = 111) and the median of the single valid rounds (n=9) remained at 13.76 ‰ and the median of the labs at 13.79 ‰ (n=5). Excluding NBS127 from the normalization slightly reduced the δ<sup>18</sup>O value to 13.74 ± 0.31 ‰ (n = 111). The BOKU Ag<sub>3</sub>PO<sub>4</sub> comparison material is available for stable isotope research laboratories to facilitate the calibration of their lab comparison material.</p><p> </p><p>Brand, W.A., Coplen, T.B., Aerts-Bijma, A.T., Böhlke, J.K., Gehre, M., Geilmann, H., Gröning, M., Jansen, H.G., Meijer, H.A.J., Mroczkowski, S.J., Qi, H., Soergel, K., Stuart-Williams, H., Weise, S.M., Werner, R.A., 2009. Comprehensive inter-laboratory calibration of reference materials for δ<sup>18</sup>O versus VSMOW using various on-line high-temperature conversion techniques. Rapid Communications in Mass Spectrometry, 999–1009. doi:10.1002/rcm</p><p>Paul, D., Skrzypek, G., Fórizs, I., 2007. Normalization of measured stable isotopic compositions to isotope reference scales - A review. Rapid Communications in Mass Spectrometry 21, 3006–3014. doi:10.1002/rcm.3185</p>

scholarly journals Medidas de Tendência Central: Análise da Qualidade das Questões do ENEM de 2016 a 2018

2021 ◽  
Vol 14 (1) ◽  
pp. 119-128
Author(s):  
Talita Emidio Andrade Soares ◽  
Denilson Junio Marques Soares ◽  
Wagner Dos Santos
Keyword(s):  
High School ◽  
Quality Evaluation ◽  
Basic Education ◽  
Item Analysis ◽  
Arithmetic Mean ◽  
Central Tendency ◽  
Weighted Arithmetic ◽  
Evaluation Policies ◽  
Teaching Learning ◽  
Different Levels

ResumoO Exame Nacional do Ensino Médio (ENEM) tem se constituido como uma das principais políticas de avaliação da qualidade da educação básica brasileira. A expansão do exame e as atribuições a ele investidas tornaram imprescindíveis as discussões acerca da sua estrutura e qualidade. Com o intuito de contribuir para esta temática, este artigo tem o objetivo de analisar a qualidade de 11 itens de Matemática das provas do ENEM de 2016 a 2018, que se referem às Medidas de Tendência Central: média aritmética simples e ponderada, mediana e moda. Para isto, adotou-se uma metodologia predominantemente quantitativa e exploratória, desenvolvida a partir da aplicação de técnicas psicométricas a uma amostra representativa de participantes do exame. Os resultados apontaram para itens adequados e bem estruturados, que privilegiam o raciocínio lógico e a interpretação. A análise pedagógica indicou para a comum confusão entre os conceitos de média aritmética simples e ponderada, que representam a grande maioria dos itens analisadas. Espera-se que os resultados obtidos possam esclarecer alguns conceitos da psicometria e auxiliar no processo de ensino e aprendizagem de estatística na educação básica. Palavras-chave: Medidas de Tendência Central. Psicometria. Análise de Itens. ENEM. AbstractThe National High School Examination (ENEM) has become one of the most of the main Brazilian quality evaluation policies in the field of basic education. The expansion and attributions invested in the test make indispensable the discussions about its structure and quality. In order to contribute to this theme, we propose to analyze 11 Maths questions to ENEM from 2016 to 2018 and related to Measures of Central Tendency: arithmetic mean; weighted arithmetic mean, median and mode. It was used a quantitative and exploratory methodology, developed through psychometrics methods applied to a significant sample of students that made the exam. The results pointed to well-structured items, that favor logical reasoning and interpretation and that have an excellent ability discriminate groups with different levels of. Its highlight the confusion between concepts of arithmetic mean and weighted arithmetic mean, that represent the most of the questions analyzed. It is hoped that this research may help clarify some concepts of psychometry and can assist in the teaching-learning process of statistics in basic education.Keywords: Measures of Central Tendency. Psychometry. Item Analysis. ENEM.

IFRSs Convergence and Expectation Gap: Vindication from Practitioners

Metamorphosis ◽  
2018 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
Rajat Deb ◽  
Joydeep Das
Keyword(s):  
Online Survey ◽  
Reliability And Validity ◽  
Arithmetic Mean ◽  
Regulatory Requirements ◽  
Reporting Practices ◽  
Weighted Arithmetic ◽  
Expectation Gap ◽  
Mean Differences ◽  
Practical Implications ◽  
Statistical Results

The study has attempted to measure the Indian practitioners’ expectation gaps about IFRSs convergence. Based on literature, two hypotheses, a conceptual model and a questionnaire, have been formed. Through protocol interviews followed by a pretest, the questionnaire has been tested (reliability and validity) before conducting the online survey. A total of 159 sample responses has been assessed to measure the gaps on four major parameters. For assaying the gaps, the arithmetic and weighted arithmetic mean differences and paired sample t-test have been applied, which have indicated the likely persistence of gaps. The significant statistical results have indicated likely to reject the null hypotheses and it has to conclude that regulatory requirements have influenced in convergence and the Ind AS probably to improve the reporting practices, audit qualities and analysts’ forecasting. Study limitations, practical implications and roadmap for further research have also been indicated.

Interval basic uncertain information and related aggregations in decision making

2021 ◽  
pp. 1-8
Author(s):  
LeSheng Jin ◽  
Radko Mesiar ◽  
Ronald Yager ◽  
Sema Kayapinar Kaya
Keyword(s):  
Decision Making ◽  
Arithmetic Mean ◽  
Information Environment ◽  
Uncertain Information ◽  
Rule Based ◽  
Weighted Arithmetic ◽  
Multi Criteria Evaluation

The recently proposed basic uncertain information can directly present numerical uncertainties for given real values, but it cannot handle given interval values which themselves also have uncertainties. Against this background, this work proposes the concept of interval basic uncertain information which serves as a generalization of basic uncertain information and involves two types of uncertainties. We analyze some basic operations, weighted arithmetic mean and preference transformation for interval basic uncertain information. The Rule-based decisions and the comprehensive certainty of interval basic uncertain information are also discussed. An illustrative example of multi-source multi-criteria evaluation under interval basic uncertain information environment is presented.

scholarly journals Bedload transport in two creeks at the ice-free area of the Baranowski Glacier, King George Island, West Antarctica

2017 ◽  
Vol 38 (1) ◽  
pp. 21-39 ◽  
Author(s):  
Joanna Sziło ◽  
Robert J. Bialik
Keyword(s):  
Water Discharge ◽  
Weather Conditions ◽  
Arithmetic Mean ◽  
Bedload Transport ◽  
Water Levels ◽  
West Antarctica ◽  
Weighted Arithmetic ◽  
Granulometric Analysis ◽  
First Time

Abstract This paper presents a unique case study and methodology for measurements of the bedload transport in the two, newly created troughs at the forefield of the Baranowski Glacier: Fosa and Siodło creeks. The weather conditions and the granulometric analysis are presented and discussed briefly. Rating curves for the Fosa and Siodło creeks are presented for the first time for this region. Changes of the bedload transport as well as water discharge and water velocity at both creeks are investigated. The hysteresis for the relationships between rate of bedload transport and water discharges were identified showing that for both creeks for the higher water levels a figure of eight loop may be easily recognized. Moreover, a new method for the calculation of bedload transport rate, based on the weighted arithmetic mean instead of the arithmetic mean, is proposed.

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