The trivariate normal distribution: partial and multiple correlations and regressions

1999 ◽  
pp. 188-196
Author(s):  
Pierre Jolicoeur
Keyword(s):  
Normal Distribution ◽  
Trivariate Normal

A procedure to develop a backbone ground-motion model: A case study for its implementation

2021 ◽  
pp. 875529302110145
Author(s):  
Sinan Akkar ◽  
Özkan Kale ◽  
M Abdullah Sandıkkaya ◽  
Emrah Yenier
Keyword(s):  
Normal Distribution ◽  
Ground Motion ◽  
Epistemic Uncertainty ◽  
Motion Model ◽  
Logic Tree ◽  
Ground Motion Model ◽  
Stable Continental Region ◽  
Trivariate Normal ◽  
Motion Characterization

The backbone modeling in ground-motion characterization (GMC) is a useful methodology to describe the epistemic uncertainty in median ground-motion predictions. The approach uses a backbone ground-motion model (GMM) and populates the GMC logic tree with the scaled and/or adjusted versions of the backbone GMM to capture the epistemic uncertainty in median ground motions. The scaling and/or adjustment should represent the specific features and uncertainties involved in source, path, and site effects at the target site. The identification of the backbone model requires different considerations specific to the nature of the ground-motion hazard problem. In this article, we present a scaled backbone modeling approach that considers the magnitude- and distance-scaling predictors as well as their correlation to address the epistemic uncertainty in median ground-motion predictions. This approach results in a trivariate normal distribution to fully define a range of epistemic uncertainty in a model sample space. The simultaneous consideration of magnitude and distance scaling while defining the epistemic uncertainty and the methodology followed for the simplified representation of trivariate normal distribution in ground-motion logic tree are the two important features in our procedure. We first present the proposed approach that is followed by a case study for Central and Eastern North America (CENA) stable continental region. The case study discusses the underlying assumptions and limitations of the proposed approach.

A Probabilistic Model for the Determination of Acid Rain Levels

1993 ◽  
Vol 28 (2) ◽  
pp. 337-354 ◽  
Author(s):  
Serge B. Provost ◽  
Rajesh K. Barnwal
Keyword(s):  
Normal Distribution ◽  
Probabilistic Model ◽  
Concentration Distribution ◽  
Three Dimensional ◽  
Elliptical Cylinder ◽  
Gaussian Fields ◽  
Rain Drops ◽  
Trivariate Normal ◽  
Elliptical Cylinders

Abstract This article gives, in closed form, exact representations of the probability content of elliptical cylinders lying in three-dimensional Gaussian fields. The concentration of a pollutant present in the air, in a given neighborhood, is assumed to follow a trivariate normal distribution. Noting that the amount of a certain pollutant absorbed by a cluster of clouds—whose volume is approximated by an ellipsoid—is proportional to the pollutant’s integrated concentration distribution over the elliptical cylinder that the cluster sweeps out, and that the trajectories of the rain drops coming from this cluster also fill an elliptical cylinder, one could, for example, use the derived results to determine the amount of sulphuric acid deposited on a given area of the earth’s surface during rainfall.

Estimation of parameters in a truncated trivariate normal distribution

Psychometrika ◽  
1950 ◽  
Vol 15 (4) ◽  
pp. 339-347 ◽  
Author(s):  
D. F. Votaw ◽  
J. A. Rafferty ◽  
W. L. Deemer
Keyword(s):  
Normal Distribution ◽  
Estimation Of Parameters ◽  
Trivariate Normal

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Interrelations of Thrombo-Embolic Diseases and Blood-Group Distribution

1963 ◽  
Vol 09 (02) ◽  
pp. 472-474 ◽  
Author(s):  
W Dick ◽  
W Schneider ◽  
K Brockmüller ◽  
W Mayer
Keyword(s):  
Normal Distribution ◽  
Blood Group ◽  
Blood Groups ◽  
The Other ◽  
Other Hand ◽  
Group Distribution

SummaryA comparison between the repartition of the blood groups in 461 patients suffering from thromboembolic disorders and the normal distribution has shown a statistically ascertained predominance of the group A1. On the other hand the blood groups 0 and A2 are distinctly less frequent than in the normal distribution.

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