Alternate Forms and Computational Considerations for Numerical Evaluation of Cumulative Probability Distributions Directly from Characteristic Functions

1970 ◽  
Author(s):  
Albert H. Nuttall
Keyword(s):  
Numerical Evaluation ◽  
Probability Distributions ◽  
Characteristic Functions ◽  
Cumulative Probability ◽  
Alternate Forms

Opposite Effects for Cations in Enhancing and Suppressing Nucleation of Pathology Crystallization of Gout

CrystEngComm ◽  
2021 ◽  
Author(s):  
anqi da ◽  
aijun ren ◽  
Rong Chen ◽  
Xingde Zhang ◽  
yonglan pan ◽  
...  
Keyword(s):  
Probability Distributions ◽  
Crystal Nucleation ◽  
Cumulative Probability ◽  
Monosodium Urate

In this paper, we focused on the influence of common serum cations on monosodium urate monohydrate (MSUM) crystals nucleation determined from cumulative probability distributions (CPD) of the solute crystal nucleation...

MATHEMATICAL MODELLING OF FORECASTING THE RESULTS OF KNOWLEDGE TESTING / ŽINIŲ TIKRINIMO REZULTATŲ PROGNOZĖS MATEMATINIS MODELIAVIMAS

2008 ◽  
Vol 14 (3) ◽  
pp. 388-401 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Natalja Kosareva
Keyword(s):  
Item Response ◽  
Logistic Model ◽  
Probability Distributions ◽  
Characteristic Functions ◽  
Test Results ◽  
Test Items ◽  
Mathematics Test ◽  
Level Method ◽  
Selection For ◽  
Selection Of

In this paper a mathematical model for obtaining probability distribution of the knowledge testing results is proposed. Differences and similarities of this model and Item Response Theory (IRT) logistic model are discussed. Probability distributions of 10 items test results for low, middle and high ability populations selecting characteristic functions of the various difficulty items combinations are obtained. Entropy function values for these items combinations are counted. These results enable to formulate recomendations for test items selection for various testing groups according to their attainment level. Method of selection of a suitable item characteristic function based on the Kolmogorov compatibility test, is proposed. This method is illustrated by applying it to a discreet mathematics test item. Santrauka Straipsnyje pasiūlytas matematinis modelis žinių tikrinimo rezultatų tikimybiniam skirstiniui gauti. Aptarti šio modelio ir užduočių sprendimo teorijos (IRT) logistinio modelio skirtumai ir panašumai. Išnagrinėti 10 klausimų testo rezultatų tikimybiniai skirstiniai silpnai, vidutinei ir stipriai testuojamųjų populiacijoms parenkant įvairias testo klausimų sunkumo funkcijų kombinacijas. Apskaičiuotos entropijos funkcijos reikšmės. Gauti rezultatai leidžia formuluoti rekomendacijas testo klausimams parinkti skirtingoms testuojamųjų grupėms pagal jų žinių lygį. Pasiūlytas tinkamiausios klausimo charakteristinės funkcijos parinkimo būdas, grindžiamas Kolmogorovo kriterijumi. Ši procedūra iliustruojama taikant ją konkrečiam diskrečiosios matematikos testo klausimui.

A Comparison of Probability Bounds Analysis and Sensitivity Analysis in Environmentally Benign Design and Manufacture

2006 ◽  
Author(s):  
Jason Matthew Aughenbaugh ◽  
Scott Duncan ◽  
Christiaan J. J. Paredis ◽  
Bert Bras
Keyword(s):  
Sensitivity Analysis ◽  
Epistemic Uncertainty ◽  
Probability Distributions ◽  
Environmentally Benign ◽  
Cumulative Probability ◽  
Uncertain Parameters ◽  
Probability Bounds ◽  
Irreducible Uncertainty ◽  
Design And Manufacture ◽  
Selection Of

There is growing acceptance in the design community that two types of uncertainty exist: inherent variability and uncertainty that results from a lack of knowledge, which variously is referred to as imprecision, incertitude, irreducible uncertainty, and epistemic uncertainty. There is much less agreement on the appropriate means for representing and computing with these types of uncertainty. Probability bounds analysis (PBA) is a method that represents uncertainty using upper and lower cumulative probability distributions. These structures, called probability boxes or just p-boxes, capture both variability and imprecision. PBA includes algorithms for efficiently computing with these structures under certain conditions. This paper explores the advantages and limitations of PBA in comparison to traditional decision analysis with sensitivity analysis in the context of environmentally benign design and manufacture. The example of the selection of an oil filter involves multiple objectives and multiple uncertain parameters. These parameters are known with varying levels of uncertainty, and different assumptions about the dependencies between variables are made. As such, the example problem provides a rich context for exploring the applicability of PBA and sensitivity analysis to making engineering decisions under uncertainty. The results reveal specific advantages and limitations of both methods. The appropriate choice of an analysis depends on the exact decision scenario.

THE UNDISCOVERED OIL AND GAS POTENTIAL OF AUSTRALIA

1983 ◽  
Vol 23 (1) ◽  
pp. 27
Author(s):  
B.G. McKAY
Keyword(s):  
Oil And Gas ◽  
Probability Distributions ◽  
Time Frame ◽  
Cumulative Probability ◽  
Resource Base ◽  
Computer Based ◽  
Discovery Time ◽  
The Individual ◽  
Gas Potential

In 1982 Esso Australia completed a fundamental re-assessment of the undiscovered oil and gas potential of Australia. In the seven years since Esso's previous major study there has been a marked upsurge in exploration for hydrocarbons, particularly oil. During this period several hundred wells have been drilled and hundreds of thousands of kilometres of seismic data have been recorded. New discoveries of both oil and gas have been made in several areas. Because of this influx of new data, a re-assessment was considered timely.The assessment utilised computer-based techniques and incorporated improvements in assessment and risk theory. The study involved the identification of more than one hundred individual plays followed by the volumetric and risk assessment of those plays. The risked assessments of the individual plays were then combined to produce an overall assessment for Australia in the form of cumulative probability distributions for oil and gas.The results show that the potential exists in Australia to find a significant volume of additional oil, possibly equivalent to the amount of oil discovered to date. The assessment also indicates a high probability of abundant undiscovered gas.Although the perceived resource base is quite encouraging, no consideration was given in the assessment to operational, economic or political constraints. Consequently there is no discovery time-frame implied within the assessment results. The rate of discovery will be determined by the amount and quality of exploration effort, which in turn will be dictated by the economic and political environment under which industry is allowed to operate.

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