The Influence of Shape on Iceberg Wave-Induced Velocity Statistics

1990 ◽  
Vol 112 (3) ◽  
pp. 263-269 ◽  
Author(s):  
J. H. Lever ◽  
D. Sen ◽  
D. Attwood
Keyword(s):  
Risk Analysis ◽  
Random Variables ◽  
Random Variable ◽  
Response Spectra ◽  
Offshore Structures ◽  
Linear Superposition ◽  
Sea State ◽  
Motion Response ◽  
Velocity Statistics ◽  
Wave Induced

The motion response of small icebergs in waves has been the subject of recent investigation to provide information for the design of offshore structures resistant to glacial ice impact. Since sea state and iceberg size are random variables, probabilistic formulations have been developed for use in risk analysis-based design procedures. The present work discusses the influence of iceberg shape on its motion response in waves. Wave tank tests were conducted which show that model shape has a significant effect on wave-induced ice motion. For all models tested, however, response spectra in an irregular sea could be accurately estimated using the linear superposition of measured responses in regular waves and the measured wave energy spectra. This was true in spite of obvious nonlinear behavior exhibited in high model seas. The observed differences in wave-induced motion for differently shaped models with similar masses and characteristic lengths suggest that iceberg shape should also be treated as a random variable in probabilistic formulations. In this way, wave-induced ice motion may be represented as a function of sea state, iceberg mass or characteristic length, and iceberg shape, all random variables. An earlier risk analysis formulation is extended to incorporate the influence of randomly varying iceberg shape on ice/structure impact velocity statistics.

A Method to Upgrade Iceberg Velocity Statistics to Include Wave-Induced Motion

1987 ◽  
Vol 109 (3) ◽  
pp. 278-286 ◽  
Author(s):  
J. H. Lever ◽  
D. Sen
Keyword(s):  
Three Dimensional ◽  
Interaction Model ◽  
Environmental Parameters ◽  
Offshore Structures ◽  
Grand Banks ◽  
Drilling Rig ◽  
Velocity Statistics ◽  
Impact Risk ◽  
Induced Motion ◽  
Wave Induced

Iceberg impact design loads for offshore structures can be estimated by incorporating an ice/structure interaction model in a probabilistic framework, or risk analysis. The relevant iceberg and environmental parameters are input in statistical form. Iceberg velocity statistics are usually compiled from drilling rig radar reports, and hence represent estimates of average hourly drift speeds. Yet it is the instantaneous ice velocity which is the relevant input to the simulation of the iceberg/structure collision process. Thus, risk analyses based on mean drift speed distributions will only yield valid results for the subset of conditions where wave-induced iceberg motion is negligible. This paper describes a method which, for the first time, systematically accounts for wave-induced motion in iceberg impact risk analyses. A linear three-dimensional potential flow model is utilized to upgrade iceberg velocity statistics to include the influence of Grand Banks sea-state conditions on instantaneous ice motion. The results clearly demonstrate the importance of including wave-induced motion in iceberg impact risk analyses.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

scholarly journals Fully degenerate Bell polynomials associated with degenerate Poisson random variables

2021 ◽  
Vol 19 (1) ◽  
pp. 284-296
Author(s):  
Hye Kyung Kim
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Combinatorial Identities ◽  
Bell Polynomials ◽  
Poisson Random Variable ◽  
Central Moments ◽  
Special Polynomials ◽  
Special Numbers And Polynomials ◽  
New Type ◽  
Two Parameters

Abstract Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the fully degenerate Bell polynomials. We derive some combinatorial identities for the fully degenerate Bell polynomials related to the n n th moment of the degenerate Poisson random variable, special numbers and polynomials. In the second part, we consider the fully degenerate Bell polynomials associated with degenerate Poisson random variables with two parameters α > 0 \alpha \gt 0 and β > 0 \beta \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the two-variable fully degenerate Bell polynomials. We show their connection with the degenerate Poisson central moments, special numbers and polynomials.

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

INFORMATION AND UNCERTAINTY IN A QUEUING SYSTEM

2007 ◽  
Vol 21 (3) ◽  
pp. 361-380 ◽  
Author(s):  
Refael Hassin
Keyword(s):  
Service Quality ◽  
Random Variables ◽  
Random Variable ◽  
Queuing System ◽  
Service Rate ◽  
Single Server ◽  
Profit Function

This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.

The central limit problem for trimmed sums

1987 ◽  
Vol 102 (2) ◽  
pp. 329-349 ◽  
Author(s):  
Philip S. Griffin ◽  
William E. Pruitt
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Limit Problem ◽  
Absolute Value ◽  
Trimmed Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Central Limit Problem ◽  
Trimmed Sum

Let X, X1, X2,… be a sequence of non-degenerate i.i.d. random variables with common distribution function F. For 1 ≤ j ≤ n, let mn(j) be the number of Xi satisfying either |Xi| > |Xj|, 1 ≤ i ≤ n, or |Xi| = |Xj|, 1 ≤ i ≤ j, and let (r)Xn = Xj if mn(j) = r. Thus (r)Xn is the rth largest random variable in absolute value from amongst X1, …, Xn with ties being broken according to the order in which the random variables occur. Set (r)Sn = (r+1)Xn + … + (n)Xn and write Sn for (0)Sn. We will refer to (r)Sn as a trimmed sum.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

Stability of offshore structures in shallow water depth

2011 ◽  
Vol 2 (2) ◽  
pp. 320-333
Author(s):  
F. Van den Abeele ◽  
J. Vande Voorde
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Fossil Fuels ◽  
Oil And Gas ◽  
Structural Response ◽  
Offshore Structures ◽  
Exploration And Production ◽  
Subsea Pipelines ◽  
Wave Induced ◽  
Shallow Water Depth

The worldwide demand for energy, and in particular fossil fuels, keeps pushing the boundaries of offshoreengineering. Oil and gas majors are conducting their exploration and production activities in remotelocations and water depths exceeding 3000 meters. Such challenging conditions call for enhancedengineering techniques to cope with the risks of collapse, fatigue and pressure containment.On the other hand, offshore structures in shallow water depth (up to 100 meter) require a different anddedicated approach. Such structures are less prone to unstable collapse, but are often subjected to higherflow velocities, induced by both tides and waves. In this paper, numerical tools and utilities to study thestability of offshore structures in shallow water depth are reviewed, and three case studies are provided.First, the Coupled Eulerian Lagrangian (CEL) approach is demonstrated to combine the effects of fluid flowon the structural response of offshore structures. This approach is used to predict fluid flow aroundsubmersible platforms and jack-up rigs.Then, a Computational Fluid Dynamics (CFD) analysis is performed to calculate the turbulent Von Karmanstreet in the wake of subsea structures. At higher Reynolds numbers, this turbulent flow can give rise tovortex shedding and hence cyclic loading. Fluid structure interaction is applied to investigate the dynamicsof submarine risers, and evaluate the susceptibility of vortex induced vibrations.As a third case study, a hydrodynamic analysis is conducted to assess the combined effects of steadycurrent and oscillatory wave-induced flow on submerged structures. At the end of this paper, such ananalysis is performed to calculate drag, lift and inertia forces on partially buried subsea pipelines.

scholarly journals On Exact Sampling of Nonnegative Infinitely Divisible Random Variables

2012 ◽  
Vol 44 (3) ◽  
pp. 842-873 ◽  
Author(s):  
Zhiyi Chi
Keyword(s):  
Basic Result ◽  
Random Variables ◽  
Random Variable ◽  
Fixed Number ◽  
Rejection Sampling ◽  
Infinitely Divisible ◽  
Exact Sampling ◽  
Special Cases ◽  
Wide Range ◽  
Lévy Density

Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on X ≤ r can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

scholarly journals Improving the Asmussen–Kroese-Type Simulation Estimators

2012 ◽  
Vol 49 (4) ◽  
pp. 1188-1193 ◽  
Author(s):  
Samim Ghamami ◽  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Nonnegative Integer ◽  
Rare Event ◽  
Random Variables ◽  
Random Variable ◽  
Heavy Tailed ◽  
Independent Identically Distributed

The Asmussen–Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,…,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

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