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Practitioner advice: Approximation of the cumulative density of left-sided truncated normal distribution using logistic function and its implementation in Microsoft Excel

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QUALITY ENGINEERING 2017年第2期29卷 322-328页

作者： Hamasha, Mohammad M. Prince Sultan Univ Dept Engn Management POB 66833 Riyadh 11586 Saudi Arabia

The left-sided truncated normal distribution is especially important in quality engineering where we remove the left side of the distribution, for example, due to estimation of the life of used products. Although the theoretical background of truncated normal distribution is already established, there is very little work on mathematical approximation of the probability density and the cumulative probability density functions. In this article, a high accuracy mathematical approximation of the left-sided truncated normal distribution is proposed. A full analysis of errors and recommendations for implementation using Microsoft Excel are provided at the end of this article.

关键词： cumulative probability function distribution error function errors analysis logistic distribution logistic function mathematical approximation normal distribution probability function truncated normal distribution

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The use of generation stochastic models to study an epidemic disease

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ADVANCES IN DIFFERENCE EQUATIONS 2013年第1期2013卷 1-9页

作者： Chaharborj, S. Seddighi Fudziah, I. Abu Bakar, M. R. Chaharborj, R. Seddighi Majid, Z. A. Ahmad, A. G. B. Univ Putra Malaysia Fac Sci Dept Math Upm 43400 Selangor Malaysia Nucl Sci & Technol Res Inst Plasma Phys & Nucl Fus Res Sch Tehran Iran Islamic Azad Univ Bushehr Branch Dept Math Sci & Res Branch Bushehr Iran Eastern Mediterranean Univ Dept Appl Math & Comp Sci Gazimagusa Northern Cyprus Cyprus Univ Putra Malaysia Inst Math Res Selangor Darul Ehsan Selangor Malaysia Univ Kebangsaan Malaysia Fac Sci & Technol Sch Math Ukm Bangi 43600 Selangor Malaysia

' Stochastic models have an important role in modeling and analyzing epidemic diseases for small size population. In this article, we study the generation of stochastic models for epidemic disease susceptible-infective-susceptible model. Here, we use the separation variable method to solve partial differential equation and the new developed modified probability generating function (PGF) of a random process to include a random catastrophe to solve the ordinary differential equations generated from partial differential equation. The results show that the probability function is too sensitive to mu, beta and gamma parameters.

关键词： epidemic diseases susceptible-infective-susceptible deterministic model stochastic model probability function

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Exchangeable trait allocations

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ELECTRONIC JOURNAL OF STATISTICS 2018年第2期12卷 2290-2322页

作者： Campbell, Trevor Cai, Diana Broderick, Tamara MIT CSAIL 77 Massachusetts Ave Cambridge MA 02139 USA Princeton Univ Dept Comp Sci Princeton NJ 08544 USA

Trait allocations are a class of combinatorial structures in which data may belong to multiple groups and may have different levels of belonging in each group. Often the data are also exchangeable, i.e., their joint distribution is invariant to reordering. In clustering-a special case of trait allocation-exchangeability implies the existence of both a de Finetti representation and an exchangeable partition probability function (EPPF), distributional representations useful for computational and theoretical purposes. In this work, we develop the analogous de Finetti representation and exchangeable trait probability function (ETPF) for trait allocations, along with a characterization of all trait allocations with an ETPF. Unlike previous feature allocation characterizations, our proofs fully capture single-occurrence "dust" groups. We further introduce a novel constrained version of the ETPF that we use to establish an intuitive connection between the probability functions for clustering, feature allocations, and trait allocations. As an application of our general theory, we characterize the distribution of all edge-exchangeable graphs, a class of recently-developed models that captures realistic sparse graph sequences.

关键词： Trait allocation exchangeability paintbox probability function partition feature allocation graph vertex allocation edge exchangeability

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Investigation of green-glued laminated timber from the Congo Basin: durability, mechanical strength and variability trends of the bondlines

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SOUTHERN FORESTS-A JOURNAL OF FOREST SCIENCE 2022年第3期84卷 225-241页

作者： Lissouck, Rene Oum Mvondo, Rachel Raissa Ngono Ateba, Francois Rene Pommier, Regis Univ Yaounde I Natl Adv Sch Engn Lab Civil Engn & Mech Yaounde Cameroon Univ Yaounde I Inst Wood Technol Mbalmayo Cameroon Univ Yaounde I Natl Adv Sch Engn Lab L3E Energy Water & Environm Yaounde Cameroon Univ Bordeaux Talence France

The development of glulam may give complementary, added-value to an important part of the timber production in the Congo Basin. Nevertheless, the high humidity in which these timbers operate may cause problems such as cracks and severe deformations if they are not suitably bonded. Moreover, there is a lack of knowledge concerning the refined design of the bondlines of glulam assembling from the Congo Basin hardwoods. We investigated the durability, mechanical strength, and variability features of the bondlines, manufactured under higher moisture conditions. Eight hardwood species with very different properties were selected. A one-component polyurethane adhesive was used. Industrial gluing parameters were kept constant. Delamination, shear tests and analysis of bondlines thickness were carried out. Multivariate analysis and a goodness-of-fit test of the strength variability of the bondlines were performed. Optimum bondlines thicknesses were obtained. Their durability exhibited satisfactory trends up to a density of 750 kg/m3. The behaviour of the bondlines can operate in three homogeneous groups. In each of them, the variability of the shear strength can be properly modelled using a 3-parameter Weibull probability. Wood failure trends were in accordance with several international requirements. The density value of 750 kg/m3 appeared as critical for the compatibility between the shear strength, the durability and the bondlines thickness. The overall results showed the ability of several tropical timber species to be valorised in green-glulam applications. Moreover, the findings unlock new trends concerning a reliable and safe design of tropical glulam as a structural wood-based product.

关键词： bondability bondlines design Cameroon durability hardwood probability function shear strength tropical glulam

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Influence of analytical bias and imprecision on the number of false positive results using Guideline-Driven Medical Decision Limits

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CLINICA CHIMICA ACTA 2014年 430卷 1-8页

作者： Petersen, Per Hyltoft Klee, George G. Univ Bergen Fac Med & Dent Norwegian Qual Improvement Primary Care Labs NOKL Sect Gen PracticeDept Publ Hlth & Primary Hlth C N-5892 Bergen Norway Mayo Clin Dept Lab Med & Pathol Rochester MN USA

Background: Diagnostic decisions based on decision limits according to medical guidelines are different from the majority of clinical decisions due to the strict dichotomization of patients into diseased and non-diseased. Consequently, the influence of analytical performance is more critical than for other diagnostic decisions where much other information is included. The aim of this opinion paper is to investigate consequences of analytical quality and other circumstances for the outcome of "Guideline-Driven Medical Decision Limits". Terms: Effects of analytical bias and imprecision should be investigated separately and analytical quality specifications should be estimated accordingly. Biological variation and analytical performance: Use of sharp decision limits doesn't consider biological variation and effects of this variation are closely connected with the effects of analytical performance. Such relationships are investigated for the guidelines for HbA(1c) in diagnosis of diabetes and in risk of coronary heart disease based on serum cholesterol. The effects of a second sampling in diagnosis give dramatic reduction in the effects of analytical quality showing minimal influence of imprecision up to 3 to 5% for two independent samplings, whereas the reduction in bias is more moderate and a 2% increase in concentration doubles the percentage of false positive diagnoses, both for HbA(1c) and cholesterol. Frequency of follow-up laboratory tests: An alternative approach comes from the current application of guidelines for follow-up laboratory tests according to clinical procedure orders, e.g. frequency of parathyroid hormone requests as a function of serum calcium concentrations. Here, the specifications for bias can be evaluated from the functional increase in requests for increasing serum calcium concentrations. probability function for diagnoses: In consequence of the difficulties with biological variation and the practical utilization of concentration dependence of

关键词： Analytical bias Analytical imprecision Analytical quality specifications Clinical guidelines Clinical outcome probability function

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Modeling prognostic factors for poor neurological outcome in conservatively treated patients with intracerebral hemorrhage: A focus on TNF-α

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CLINICAL NEUROLOGY AND NEUROSURGERY 2018年 172卷 51-58页

作者： Rendevski, Vladimir Aleksovski, Boris Stojanov, Dragan Rendevska, Ana Mihajlovska Aleksovski, Vasko Gjorgoski, Icko Ss Cyril & Methodius Univ Univ Clin Neurosurg Med Fac Mother Teresa 17 Skopje 1000 Macedonia Ss Cyril & Methodius Univ Fac Nat Sci & Math Arhimedova 3POB 162 Skopje 1000 Macedonia Univ Nis Fac Med Dr Zoran Djindjic Blvd 81 Nish 18000 Serbia Ss Cyril & Methodius Univ Univ Clin Radiol Med Fac Belgradska Bb Skopje 1000 Macedonia Ss Cyril & Methodius Univ Univ Clin Neurol Med Fac Mother Teresa 17 Skopje 1000 Macedonia

Objective: Prognostic models for Intracerebral hemorrhage (ICH), mainly based on clinical evaluation, have remained inherently confounded by subjective scoring assessments and limited accuracy. In this study, we aimed at assessing the risk for poor outcome after ICH based on peripheral biochemical markers (TNF-alpha, glutamate and glucose) and radiological variables (both at admission and five days after patient's care), for modeling purposes of prognostication. Patients and Methods: The defined initial variables of fifty non-comatose conservatively treated ICH patients without severe complications during the hospitalization process (as intraventricular bleeding, or hematoma expansion) were aligned with the evaluated parameters during re-evaluation (3 months later). A comprehensive statistical approach has been applied by using different modeling strategies for prediction of their functional status and outcome. Results: Higher blood plasma glutamate, TNF-alpha and initial ICH volume at admission, as well as higher volumes of ICH and perihematomal edema after five days of care were significantly more likely associated with the poor outcome. Nevertheless, in all of the constructed models, TNF-alpha was estimated as the only significant predictive risk factor, thus outperforming the capacity of the initial ICH volume and the radiological variables after 5 days, both in terms of prognostication of the functional status and the 3-month neurological outcome. The constructed canonical variable that has fairly marked off the different outcomes was also mainly weighed by the admission TNF-alpha levels. For the first time, we have carefully developed probability functions for the neurological outcome as a response to the admission TNF-alpha levels;TNF-alpha levels > 110.35 pg/mL were assessed as an optimal cutoff point fairly identifying patients who will fall into the group with poor outcome. Conclusions: TNF-alpha based models and admission TNF-alpha screening might be appr

关键词： Intracerebral hemorrhage TNF-alpha Prognostication Poor outcome probability function

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LOCALIZATION OF MAGNETIC SOURCES UNDERGROUND BY A probability TOMOGRAPHY APPROACH

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PROGRESS IN ELECTROMAGNETICS RESEARCH M 2008年 3卷 27-56页

作者： Mauriello, P. Patella, D. Univ Molise Dept Sci & Technol Environm & Terr Campobasso Italy Univ Federico II Dept Phys Sci Naples Italy

A tomography method is proposed to image magnetic anomaly sources buried below a non-flat ground surface, using the expression of the total power associated with a measured magnetic field. It is shown that the total power can be written as a sum of crosscorrelation products between the magnetic field data set and the theoretical expression of the magnetic field generated by a source element of unitary strength. Then, applying Schwarz's inequality, an occurrence probability function is derived for imaging any distribution of magnetic anomaly sources in the subsurface. The tomographic procedure consists in scanning the half-space below the survey area by the unitary source and in computing the occurrence probability function at the nodes of a regular grid within the half-space. The grid values are finally contoured in order to single out the zones with high probability of occurrence of buried magnetic anomaly sources. Synthetic and field examples are discussed to test the resolution power of the proposed tomography.

关键词： .occurrence tomographic ground surface Naples Italy probability function survey area MAGNETIC SOURCES probability TOMOGRAPHY anomaly sources resolution power

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A statistical method to standardize and interpret the activity data generated by wireless biosensors in dairy cows

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JOURNAL OF AGRICULTURAL SCIENCE 2023年第5期161卷 678-685页

作者： Lee, Wang-Hee Lee, Mingyung Lee, Dae-Hyun Jung, Jae-Min Cho, Hyunjin Seo, Seongwon Chungnam Natl Univ Dept Biosyst Engn Daejeon 34134 South Korea Chungnam Natl Univ Div Anim & Dairy Sci Daejeon 34134 South Korea

Activity biosensors have been used recently to measure and diagnose the physiological status of dairy cows. However, owing to the variety of commercialized activity biosensors available in the market, activity data generated by a biosensor need to be standardized to predict the status of an animal and make relevant decisions. Hence, the objective of this study was to develop a standardization method for accommodating activity measurements from different sensors. Twelve Holstein dairy cows were monitored to collect 12 862 activity data from four types of sensors over five months. After confirming similar cyclic activity patterns from the sensors through correlation and regression analyses, the gamma distribution was employed to calculate the cumulative probability of the values of each biosensor. Then, the activity values were assigned to three levels (i.e., idle, normal and active) based on the defined proportion of each level, and the values at each level from the four sensors were compared. The results showed that the number of measurements belonging to the same level was similar, with less than a 10% difference at a specific threshold value. In addition, more than 87% of the heat alerts generated by the internal algorithm of three of the four biosensors could be assigned to the active level, suggesting that the current standardization method successfully integrated the activity measurements from different biosensors. The developed probability-based standardization method is expected to be applicable to other biosensors for livestock, which will lead to the development of models and solutions for precision livestock farming.

关键词： activity sensor dairy cow precision livestock farming probability function standardization

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SOME DISTRIBUTION PROBLEMS OF ORDER STATISTICS FROM DISCRETE POPULATIONS

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1969年第3期21卷 551-&页

作者： KABE, DG St. Mary’s University Halifax N.S. Canada

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probability issues in locality descriptions based on Voronoi neighbor relationship

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JOURNAL OF VISUAL LANGUAGES AND COMPUTING 2012年第4期23卷 213-222页

作者： Gong, Yongxi Wu, Lun Lin, Yaoyu Liu, Yu Peking Univ Inst Remote Sensing & Geog Informat Syst Beijing 100871 Peoples R China Shenzhen Grad Sch Sch Urban Planning & Management Harbin Inst Technol Shenzhen 518055 Peoples R China S China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou 510641 Peoples R China

Spatial relationships play an important role in spatial knowledge representation, such as in describing localities. However, little attention has been paid to how to describe the position of a target object (TO) with a qualitative referencing system that consists of a set of reference objects (ROs) in the locality description context. We propose a method that accounts for the differences between two scenarios in locality descriptions. This method is probabilistic and is based on the Voronoi neighbor relationship to determine candidate ROs for describing a given TO's position in the second scenario. The Voronoi neighbor relationship is adopted to determine candidate ROs of a TO and to compute the neighboring area of an RO. A probability function is presented to model the uncertainty of selecting appropriate ROs. To build locality descriptions that are consistent with commonsense, four constraints are placed on the probability function. Two probability functions based on Euclidean distance and stolen-area, and a mixed probability function that considers both Euclidean distance and stolen-area, are analyzed and compared. With the mixed probability function, we establish a method to construct the locality description of a given TO. Finally, three examples demonstrate how to select ROs to describe a TO's position. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Voronoi diagram probability function Locality description Voronoi neighbor relationship

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