Seasonal Modelling of Multivariate Distributions of Metocean Parameters

2002 ◽  
Author(s):  
Se´bastien Fouques ◽  
Dag Myrhaug ◽  
Finn Gunnar Nielsen
Keyword(s):  
Correlation Matrix ◽  
Hermite Polynomials ◽  
Statistical Information ◽  
Conditional Distributions ◽  
Multivariate Distributions ◽  
Joint Distributions ◽  
The Mean ◽  
Wave Conditions ◽  
Offshore Activities ◽  
Joint Occurrence

Statistical information about the joint occurrence of metocean parameters is of importance for many offshore activities. For instance, in marine operations, environmental limitations may be brought about by both wind and wave conditions. Thus, knowledge of their joint occurrence is important as the persistence duration and the seasonal dependence of wind and waves appear to be of large interest. However, such a modelling becomes difficult as the number of considered variables increases, especially when utilizing a common parameterization of some conditional distributions. This paper proposes a general methodology that aims at modelling seasonal joint distributions of n such parameters from their correlation structure and the n marginal distributions fitted by generalized gamma ones. Two methods are proposed in order to derive an approximate joint distribution from the modelled margins. The first one matches the correlation matrix only, whereas the second one, which is based on a multivariate Hermite polynomials expansion of the multinormal distribution, is able to match joint moments of order higher than two. However, more restrictive conditions are shown by the latter. An application to the simple example of the joint occurrence of significant wave height and the mean wind velocity at the 10m elevation is used to illustrate the methods. Eventually, examples of applications like simultaneous persistence of wind and wave conditions as well as seastate forecasting from statistics are given.

Seasonal Modeling of Multivariate Distributions of Metocean Parameters With Application to Marine Operations

2004 ◽  
Vol 126 (3) ◽  
pp. 202-212 ◽  
Author(s):  
Se´bastien Fouques ◽  
Dag Myrhaug ◽  
Finn Gunnar Nielsen
Keyword(s):  
Hermite Polynomials ◽  
Statistical Information ◽  
Conditional Distributions ◽  
Multivariate Distributions ◽  
Sea State ◽  
Joint Distributions ◽  
The Mean ◽  
Wave Conditions ◽  
Offshore Activities ◽  
Joint Occurrence

Statistical information about the joint occurrence of metocean parameters is of importance for many offshore activities. For instance, in marine operations, environmental limitations may be brought about by both wind and wave conditions. Thus, knowledge of their joint occurrence is important as the persistence duration (i.e., the duration of the sea state persistence above or beneath a given level) and the seasonal dependence of wind and waves appear to be of large interest. However, such a modeling becomes difficult as the number of considered variables increases, especially when utilizing a common parameterization of some conditional distributions. This paper proposes a general methodology that aims at modeling seasonal joint distributions of n such parameters from their correlation structure and the n marginal distributions fitted by generalized gamma ones. Two methods are proposed in order to derive an approximate joint distribution from the modeled margins. The first one matches the correlation matrix only, whereas the second one, which is based on a multivariate Hermite polynomials expansion of the multinormal distribution, is able to match joint moments of order higher than two. However, more restrictive conditions are shown by the latter. An application to the simple example of the joint occurrence of significant wave height and the mean wind velocity at the 10m elevation is used to illustrate the methods. Eventually, examples of applications like simultaneous persistence of wind and wave conditions as well as seastate forecasting from statistics are given.

SOME FEATURES OF THE EQUILIBRIUM COASTAL PROFILE FOR DIFFERENT INITIAL BED SLOPES BASED ON MODELLING STUDY

2017 ◽  
Author(s):  
Dmitry Korzinin ◽  
Dmitry Korzinin ◽  
Igor Leontiev ◽  
Igor Leontiev
Keyword(s):  
Time Scales ◽  
Wave Impact ◽  
Grain Sizes ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
The Mean ◽  
Wave Conditions ◽  
Bed Slope ◽  
Coastal Profile ◽  
Modelling Study

Modelling study of the equilibrium profiles formed on sandy coasts of different bed slopes and grain sizes under the various wave conditions was realized by using the CROSS-P and Xbeach morphodynamic models. A special criterion taking into account a total volume of bed deformations per one hour was suggested to determine the conditions of profile stabilization. For both models the time scales of equilibrium profile formation were found to be the same. However, the deformation magnitudes differed significantly. Bed deformations were computed on the whole profile length over the 200-hours duration of wave impact. It was concluded that both models predict a trend of the bed slope toward a stable value. CROSS-P model shows the widening of accumulative terrace during the profile evolution. The mean slope of the equilibrium profile was found to depend on the initial bed slope.

scholarly journals BAYESIAN INFERENCE FOR THE TANGENT PORTFOLIO

2018 ◽  
Vol 21 (08) ◽  
pp. 1850054 ◽  
Author(s):  
DAVID BAUDER ◽  
TARAS BODNAR ◽  
STEPAN MAZUR ◽  
YAREMA OKHRIN
Keyword(s):  
Bayesian Inference ◽  
Point Of View ◽  
Posterior Distributions ◽  
Conditional Distributions ◽  
Linear Combinations ◽  
Conjugate Priors ◽  
Mean And Variance ◽  
The Mean ◽  
Stochastic Representations ◽  
Mean Vector

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

NOTE ON THE VLASOV EQUATION FOR PLASMAS

1963 ◽  
Vol 41 (12) ◽  
pp. 1960-1966 ◽  
Author(s):  
Ta-You Wu ◽  
M. K. Sundaresan
Keyword(s):  
Distribution Function ◽  
Fourier Transform ◽  
Vlasov Equation ◽  
Hermite Polynomials ◽  
Infinite Matrix ◽  
Mean Square ◽  
Initial Value ◽  
Positive Ions ◽  
The Mean ◽  
The Fourier Transform

The linearized Vlasov equation is solved as an initial value problem by expanding (the Fourier components of) the distribution function in a series of Hermite polynomials in the momentum, with coefficients which are functions of time. The spectrum of frequencies is given by the eigenvalues of an infinite matrix. All the frequencies ω are real, extending from small values of order ω2 = k2(u22), where (u22) is the mean square velocity of the positive ions (of mass M), to [Formula: see text], where ω1, (u12) are the plasma frequency and mean square velocity of the electrons (of mass m). The classic work of Landau solves the Vlasov equation for (the Fourier transform of) the potential for which he obtains the "damping", whereas Van Kampen and the present writers solve the equation for (the Fourier transform of) the distribution function itself. While the present work gives results equivalent to those of Van Kampen, the method is simpler and in fact elementary.

A fully automated remote refraction system

2000 ◽  
Vol 6 (2_suppl) ◽  
pp. 16-18 ◽  
Author(s):  
Alan M Dyer ◽  
Angus H Kirk
Keyword(s):  
Statistical Information ◽  
Acceptable Level ◽  
Traditional Methods ◽  
Subjective Testing ◽  
The Subject ◽  
The Mean

Traditional methods of performing refractions depend on a trained refractionist being present with the subject and conducting an interactive form of subjective testing. A fully automated refraction system was installed in 13 optical dispensaries and after 15 months the patient and statistical information was gathered. The data from all operators were consistent and suggested a lack of operator effect on the refraction results. The mean of the SD of subjective sphere measurements was 0.2, or slightly less than a quarter dioptre, which would be an acceptable level of accuracy for ordering corrective lenses. The present study suggests an absence of operator influence on the results of the refractions and a degree of consistency and accuracy compatible with the prescription of lenses.

scholarly journals Kamen's quick clustering of participation data: A research note

1988 ◽  
Vol 19 (2) ◽  
pp. 75-78
Author(s):  
L. Pitt ◽  
D. Nel
Keyword(s):  
Pilot Study ◽  
Correlation Matrix ◽  
Peer Group ◽  
Study Data ◽  
Questionnaire Design ◽  
Research Note ◽  
Data Set ◽  
Group Participation ◽  
The Mean ◽  
Standard Deviations

This brief research note revisits a simple, but very useful clustering procedure developed by Kamen (1970), and illustrates its use in the clustering of attitudinal/perceptual data. For the purpose of illustrating the technique, perceptions of peer group participation in potentially corrupt situations in business were used as the data set. The mean responses, standard deviations and medians of 458 managers served as input for a correlation matrix from which the variables were clustered. The clusters formed by the analysis have been interpreted as 'The Insiders', 'Felons', 'Happy Holidays', 'The Fiddlers', 'A Bit on the Side', and 'The Innocents'. From the clusters identified it was evident that some situations were similar in nature. Quick clustering of the pilot study data is regarded as successful and could therefore lead to improved questionnaire design as well as the elimination of similar questions.

Explorations in statistics: confidence intervals

2009 ◽  
Vol 33 (2) ◽  
pp. 87-90 ◽  
Author(s):  
Douglas Curran-Everett
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Hypothesis Test ◽  
Statistical Information ◽  
Experimental Result ◽  
P Value ◽  
Population Parameter ◽  
True Value ◽  
Level Of Confidence ◽  
The Mean

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This third installment of Explorations in Statistics investigates confidence intervals. A confidence interval is a range that we expect, with some level of confidence, to include the true value of a population parameter such as the mean. A confidence interval provides the same statistical information as the P value from a hypothesis test, but it circumvents the drawbacks of that hypothesis test. Even more important, a confidence interval focuses our attention on the scientific importance of some experimental result.

Two Methods for Analyzing Waves in Composites with Random Microstructure

1991 ◽  
Vol 253 ◽  
Author(s):  
John R. Willis
Keyword(s):  
Variational Principle ◽  
Variational Principles ◽  
Statistical Information ◽  
Random Microstructure ◽  
Self Consistent ◽  
The Mean ◽  
Stochastic Variational Principles

ABSTRACTThe problem of calculating the mean wave in a composite with random microstructure is addressed. Exact characterizations of the problem can be given, in the form of stochastic variational principles. Substitution of simple configuration-dependent trial fields into these generates approximations which are, in a sense, ‘optimal’. It is necessary in practice to employ only trial fields which will generate, in the variational principle, no more statistical information than is actually available. Trial fields that require knowledge of two-point statistics generate equations that can also be obtained directly, through use of the QCA. The same fields can be substituted into an alternative variational principle to yield an approximation that makes use of three-point statistics – this approximation is less easy to obtain by direct reasoning. When not even two-point information is available, some more elementary approximation is needed. One such approximation, which is simple and direct in its application, is an extension to dynamics of a “self-consistent embedding” scheme which is widely used in static problems. This is also discussed, together with some illustrative results for a matrix containing inclusions and for a polycrystal.

More bounds on the expectation of a convex function of a random variable

1972 ◽  
Vol 9 (4) ◽  
pp. 803-812 ◽  
Author(s):  
Ben-Tal A. ◽  
E. Hochman
Keyword(s):  
Convex Function ◽  
Upper Bound ◽  
Random Variable ◽  
Independent Random Variables ◽  
Multivariate Distributions ◽  
Absolute Deviation ◽  
Additional Information ◽  
Wait And See ◽  
The Mean ◽  
Moment Spaces

Jensen gave a lower bound to Eρ(T), where ρ is a convex function of the random vector T. Madansky has obtained an upper bound via the theory of moment spaces of multivariate distributions. In particular, Madansky's upper bound is given explicitly when the components of T are independent random variables. For this case, lower and upper bounds are obtained in the paper, which uses additional information on T rather than its mean (mainly its expected absolute deviation about the mean) and hence gets closer to Eρ(T).The importance of having improved bounds is illustrated through a nonlinear programming problem with stochastic objective function, known as the “wait and see” problem.

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