Search results for: skew distributions

Authors: Ariful Islam, Showkat Ahmad Lone

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Statistical distributions have long been employed in the assessment of semiconductor devices and product reliability. The power function-distribution is one of the most important distributions in the modern reliability practice and can be frequently preferred over mathematically more complex distributions, such as the Weibull and the lognormal, because of its simplicity. Moreover, it may exhibit a better fit for failure data and provide more appropriate information about reliability and hazard rates in some circumstances. This study deals with estimating information about failure times of items under step-stress partially accelerated life tests for competing risk based on adoptive type-I progressive hybrid censoring criteria. The life data of the units under test is assumed to follow Mukherjee-Islam distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameters and tampering coefficient. The performances of the resulting estimators of the developed model parameters are evaluated and investigated by using a simulation algorithm.

Keywords: adoptive progressive hybrid censoring, competing risk, mukherjee-islam distribution, partially accelerated life testing, simulation study

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Authors: Tuğrul Aksoy, Hüseyin Karabıyık

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Reloading vehicles are the vehicles which are generally equipped with a crane and used to carry a stowage from a point and locate onto the vehicle or vice versa. In this study, structural analysis of a reloading vehicle was performed under the loads which are predicted to be exposed under operating conditions via the finite element method. Among the finite element analysis results, the stress and displacement distributions of the vehicle and the contact pressure distributions of the guide rings within the stabilization legs were examined. Vehicle design was improved by strengthening certain parts according to the analysis results. The analyses performed for the final design were verified by the experiments involving strain gauge measurements.

Keywords: structural analysis, reloading vehicle, crane, strain gauge

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Authors: H. Zormati, J. Chebil, J. Bel Hadj Taher

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The goal of this paper is to present an addressing scheme that allows for assigning a unique IPv6 address to each node in the Internet of Things (IoT) network. This scheme guarantees uniqueness by extracting the clock skew of each communication device and converting it into an IPv6 address. Simulation analysis confirms that the presented scheme provides reductions in terms of energy consumption, communication overhead and response time as compared to four studied addressing schemes Strong DAD, LEADS, SIPA and CLOSA.

Keywords: addressing, IoT, IPv6, network, nodes

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Authors: Adel Kara, Abdelhafid Bayadi, Hocine Terrab

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This paper presents a study of electric field distribution along of 72 kV polymeric outdoor insulators with broken sheds. Different cases of damaged insulators are modeled and both of clean and polluted cases. By 3D finite element analysis using the software package COMSOL Multiphysics 4.3b. The obtained results of potential and the electrical field distribution around insulators by 3D simulation proved that finite element computations is useful tool for studying insulation electrical field distribution.

Keywords: electric field distributions, insulator, broken sheds, potential distributions

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Authors: Alireza Shayegan, Morteza Amirabadi

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The y tool was developed to quantitatively compare dose distributions, either measured or calculated. Before computing ɣ, the dose and distance scales of the two distributions, referred to as evaluated and reference, are re-normalized by dose and distance criteria, respectively. The re-normalization allows the dose distribution comparison to be conducted simultaneously along dose and distance axes. Several two-dimensional images were acquired using a Scanning Liquid Ionization Chamber EPID and Extended Dose Range (EDR2) films for regular and irregular radiation fields. The raw images were then converted into two-dimensional dose maps. Transitional and rotational manipulations were performed for images using Matlab software. As evaluated dose distribution maps, they were then compared with the corresponding original dose maps as the reference dose maps.

Keywords: energetic electron, gamma function, penumbra, Matlab software

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Authors: Rachid Belhachemi, Pierre Rostan, Alexandra Rostan

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This paper develops a discrete-time option pricing model for index options. The model consists of two key ingredients. First, daily stock return innovations are driven by a continuous hidden threshold mixed skew-normal (HTSN) distribution which generates conditional non-normality that is needed to fit daily index return. The most important feature of the HTSN is the inclusion of a latent state variable with a continuum of states, unlike the traditional mixture distributions where the state variable is discrete with little number of states. The HTSN distribution belongs to the class of univariate probability distributions where parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. It has been shown empirically that this distribution outperforms its main competitor, the mixed normal (MN) distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence. Second, heteroscedasticity in the model is captured by a threeexogenous-factor GARCH model (GARCHX), where the factors are taken from the principal components analysis of various world indices and presents an application to option pricing. The factors of the GARCHX model are extracted from a matrix of world indices applying principal component analysis (PCA). The empirically determined factors are uncorrelated and represent truly different common components driving the returns. Both factors and the eight parameters inherent to the HTSN distribution aim at capturing the impact of the state of the economy on price levels since distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. The PCA identifies statistically independent factors affecting the random evolution of a given pool of assets -in our paper a pool of international stock indices- and sorting them by order of relative importance. The PCA computes a historical cross asset covariance matrix and identifies principal components representing independent factors. In our paper, factors are used to calibrate the HTSN-GARCHX model and are ultimately responsible for the nature of the distribution of random variables being generated. We benchmark our model to the MN-GARCHX model following the same PCA methodology and the standard Black-Scholes model. We show that our model outperforms the benchmark in terms of RMSE in dollar losses for put and call options, which in turn outperforms the analytical Black-Scholes by capturing the stylized facts known for index returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.

Keywords: continuous hidden threshold, factor models, GARCHX models, option pricing, risk-premium

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Authors: Zara L. Sheady

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Fluidic oscillators are being utilised in an increasing number of applications in a wide variety of areas; these include on-board vehicle cleaning systems, flow separation control on aircraft and in fluidic circuitry. With this increased use, there is a further understanding required for the mechanics of the fluidics of the fluidic oscillator and why they work in the manner that they do. ANSYS CFX has been utilized to visualise the pressure and velocity within a microfluidic feedback oscillator. The images demonstrate how the pressure vortices build within the oscillator at the points where the velocity is diverted from linear motion through the oscillator. With an enhanced understanding of the pressure and velocity distributions within a fluidic oscillator, it will enable users of microfluidics to more greatly tailor fluidic nozzles to their specification.

Keywords: ANSYS CFX, control, fluidic oscillators, mechanics, pressure, relationship, velocity

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Authors: Eva L. Sanjuán, Jacinto Martín, M. Isabel Parra, Mario M. Pizarro

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In Extreme Value Theory, inference estimation for the parameters of the distribution is made employing a small part of the observation values. When block maxima values are taken, many data are discarded. We developed a new Bayesian inference model to seize all the information provided by the data, introducing informative priors and using the relations between baseline and limit parameters. Firstly, we studied the accuracy of the new model for three baseline distributions that lead to a Gumbel extreme distribution: Exponential, Normal and Gumbel. Secondly, we considered mixtures of Normal variables, to simulate practical situations when data do not adjust to pure distributions, because of perturbations (noise).

Keywords: bayesian inference, extreme value theory, Gumbel distribution, highly informative prior

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Authors: Tasir Khan, Yejuan Wan, Kalim Ullah

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Hydrological frequency analysis has been conducted to estimate the minimum flow elevation of the Indus River in Pakistan to protect the ecosystem. The Maximum likelihood estimation (MLE) technique is used to estimate the best-fitted distribution for Minimum Ecological Flows at nine stations of the Indus River in Pakistan. The four selected distributions, Generalized Extreme Value (GEV) distribution, Generalized Logistics (GLO) distribution, Generalized Pareto (GPA) distribution, and Pearson type 3 (PE3) are fitted in all sites, usually used in hydro frequency analysis. Compare the performance of these distributions by using the goodness of fit tests, such as the Kolmogorov Smirnov test, Anderson darling test, and chi-square test. The study concludes that the Maximum Likelihood Estimation (MLE) method recommended that GEV and GPA are the most suitable distributions which can be effectively applied to all the proposed sites. The quantiles are estimated for the return periods from 5 to 1000 years by using MLE, estimations methods. The MLE is the robust method for larger sample sizes. The results of these analyses can be used for water resources research, including water quality management, designing irrigation systems, determining downstream flow requirements for hydropower, and the impact of long-term drought on the country's aquatic system.

Keywords: minimum ecological flow, frequency distribution, indus river, maximum likelihood estimation

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Authors: Rong-Tsorng Wang

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In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: catastrophe equity put options, compound distributions, nonhomogeneous Poisson process, pricing model

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Authors: Rene Valdiviezo-Issa

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In this paper, we use Mexico’s Households Income and Expenditures (ENIGH) survey to explain the behaviour that the urban-rural expenditure gap has had since Mexico’s incorporation to the North American Free Trade Agreement (NAFTA) in 1994 and we compare it with the latest available survey, which took place in 2014. We use real trimestral expenditure per capita (RTEPC) as the measure of welfare. We use quantile regressions and a quantile regression decomposition to describe the gap between urban and rural distributions of log RTEPC. We discover that the decrease in the difference between the urban and rural distributions of log RTEPC, or inequality, is motivated because of a deprivation of the urban areas, in very specific characteristics, rather than an improvement of the urban areas. When using the decomposition we observe that the gap is primarily brought about because differences in returns to covariates between the urban and rural areas.

Keywords: quantile regression, urban-rural inequality, inequality in Mexico, income decompositon

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Authors: Z. Jannoo, B. W. Yap, N. Auchoybur, M. A. Lazim

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The two common approaches to Structural Equation Modeling (SEM) are the Covariance-Based SEM (CB-SEM) and Partial Least Squares SEM (PLS-SEM). There is much debate on the performance of CB-SEM and PLS-SEM for small sample size and when distributions are non-normal. This study evaluates the performance of CB-SEM and PLS-SEM under normality and non-normality conditions via a simulation. Monte Carlo Simulation in R programming language was employed to generate data based on the theoretical model with one endogenous and four exogenous variables. Each latent variable has three indicators. For normal distributions, CB-SEM estimates were found to be inaccurate for small sample size while PLS-SEM could produce the path estimates. Meanwhile, for a larger sample size, CB-SEM estimates have lower variability compared to PLS-SEM. Under non-normality, CB-SEM path estimates were inaccurate for small sample size. However, CB-SEM estimates are more accurate than those of PLS-SEM for sample size of 50 and above. The PLS-SEM estimates are not accurate unless sample size is very large.

Keywords: CB-SEM, Monte Carlo simulation, normality conditions, non-normality, PLS-SEM

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Authors: M. Palizvan, M. T. Abadi, M. H. Sadr

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Due to variations in damage mechanisms in the microscale, the behavior of fiber-reinforced composites is nonlinear and difficult to model. To make use of computational advantages, homogenization method is applied to the micro-scale model in order to minimize the cost at the expense of detail of local microscale phenomena. In this paper, the effective stiffness is calculated using the homogenization of nonlinear behavior of a composite representative volume element (RVE) containing fiber-matrix debonding. The damage modes for the RVE are considered by using cohesive elements and contacts for the cohesive behavior of the interface between fiber and matrix. To predict more realistic responses of composite materials, different random distributions of fibers are proposed besides square and hexagonal arrays. It was shown that in some cases, there is quite different damage behavior in different fiber distributions. A comprehensive comparison has been made between different graphs.

Keywords: homogenization, cohesive zone model, fiber-matrix debonding, RVE

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Authors: Muhammad Farooq, Ahtasham Gul

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To meet the desired standard, it is important to monitor and analyze different engineering processes to get desired output. The bivariate distributions got a lot of attention in recent years to describe the randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed using two independent models developed by the nesting approach to study the effect of each component on reliability for better understanding. Further, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution, like mean median and quantile function, are discussed. We use inverse Gamma prior to study its frequentist properties by conducting Monte Carlo Markov Chain (MCMC) sampling scheme.

Keywords: reliability, system availability Weibull, inverse Lomax, Monte Carlo Markov Chain, Bayesian

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Authors: Ayesha S. Rahman, Khaled Haddad, Ataur Rahman

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At-site flood frequency analysis is used to estimate flood quantiles when at-site record length is reasonably long. In Australia, FLIKE software has been introduced for at-site flood frequency analysis. The advantage of FLIKE is that, for a given application, the user can compare a number of most commonly adopted probability distributions and parameter estimation methods relatively quickly using a windows interface. The new version of FLIKE has been incorporated with the multiple Grubbs and Beck test which can identify multiple numbers of potentially influential low flows. This paper presents a case study considering six catchments in eastern Australia which compares two outlier identification tests (original Grubbs and Beck test and multiple Grubbs and Beck test) and two commonly applied probability distributions (Generalized Extreme Value (GEV) and Log Pearson type 3 (LP3)) using FLIKE software. It has been found that the multiple Grubbs and Beck test when used with LP3 distribution provides more accurate flood quantile estimates than when LP3 distribution is used with the original Grubbs and Beck test. Between these two methods, the differences in flood quantile estimates have been found to be up to 61% for the six study catchments. It has also been found that GEV distribution (with L moments) and LP3 distribution with the multiple Grubbs and Beck test provide quite similar results in most of the cases; however, a difference up to 38% has been noted for flood quantiles for annual exceedance probability (AEP) of 1 in 100 for one catchment. These findings need to be confirmed with a greater number of stations across other Australian states.

Keywords: floods, FLIKE, probability distributions, flood frequency, outlier

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Authors: Taehan Bae

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In this paper, a class of length-biased Weibull mixtures is presented to model loss severity data. The proposed model generalizes the Erlang mixtures with the common scale parameter, and it shares many important modelling features, such as flexibility to fit various data distribution shapes and weak-denseness in the class of positive continuous distributions, with the Erlang mixtures. We show that the asymptotic tail estimate of the length-biased Weibull mixture is Weibull-type, which makes the model effective to fit loss severity data with heavy-tailed observations. A method of statistical estimation is discussed with applications on real catastrophic loss data sets.

Keywords: Erlang mixture, length-biased distribution, transformed gamma distribution, asymptotic tail estimate, EM algorithm, expectation-maximization algorithm

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Authors: Debasis Mondal, Chandan Datta, S. K. Sazim

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Quantum coherence is a key resource like entanglement and discord in quantum information theory. Wigner- Yanase skew information, which was shown to be the quantum part of the uncertainty, has recently been projected as an observable measure of quantum coherence. On the other hand, the quantum speed limit has been established as an important notion for developing the ultra-speed quantum computer and communication channel. Here, we show that both of these quantities are related. Thus, cast coherence as a resource to control the speed of quantum communication. In this work, we address three basic and fundamental questions. There have been rigorous attempts to achieve more and tighter evolution time bounds and to generalize them for mixed states. However, we are yet to know (i) what is the ultimate limit of quantum speed? (ii) Can we measure this speed of quantum evolution in the interferometry by measuring a physically realizable quantity? Most of the bounds in the literature are either not measurable in the interference experiments or not tight enough. As a result, cannot be effectively used in the experiments on quantum metrology, quantum thermodynamics, and quantum communication and especially in Unruh effect detection et cetera, where a small fluctuation in a parameter is needed to be detected. Therefore, a search for the tightest yet experimentally realisable bound is a need of the hour. It will be much more interesting if one can relate various properties of the states or operations, such as coherence, asymmetry, dimension, quantum correlations et cetera and QSL. Although, these understandings may help us to control and manipulate the speed of communication, apart from the particular cases like the Josephson junction and multipartite scenario, there has been a little advancement in this direction. Therefore, the third question we ask: (iii) Can we relate such quantities with QSL? In this paper, we address these fundamental questions and show that quantum coherence or asymmetry plays an important role in setting the QSL. An important question in the study of quantum speed limit may be how it behaves under classical mixing and partial elimination of states. This is because this may help us to choose properly a state or evolution operator to control the speed limit. In this paper, we try to address this question and show that the product of the time bound of the evolution and the quantum part of the uncertainty in energy or quantum coherence or asymmetry of the state with respect to the evolution operator decreases under classical mixing and partial elimination of states.

Keywords: completely positive trace preserving maps, quantum coherence, quantum speed limit, Wigner-Yanase Skew information

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Authors: Rao Fu, Jie Chen, Shutian Zeng, Yiping Zhuang, Agus Sudjianto

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Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper.

Keywords: conditional generative adversarial net, market and credit risk management, neural network, time series

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Authors: Javier Varillas, Jorge Alcalá

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We investigate dislocation avalanche phenomena in face-centered cubic (FCC) and body-centered cubic (BCC) crystals using massive, large-scale molecular dynamics (MD) simulations. The analysis is focused on the intermittent development of dense dislocation arrangements subjected to uniaxial tensile straining under displacement control. We employ a novel computational scheme that allows us to inject an entangled dislocation structure in periodic MD domains. We assess the emission of plastic bursts (or dislocation avalanches) in terms of the sharp stress drops detected in the stress-strain curve. The plastic activity corresponds to the sporadic operation of specific dislocation glide processes exhibiting quiescent periods between successive avalanche events. We find that the plastic intermittences in our simulations do not overlap in time under sufficiently low strain rates as dissipation operates faster than driving, where the dense dislocation networks evolve through the emission of dislocation avalanche events whose carried slip adheres to self-organized power-law distributions. These findings enable the extension of the slip distributions obtained from strict displacement-controlled micropillar compression experiments towards smaller values of slip size. Our results furnish further understanding upon the development of entangled dislocation networks in metal plasticity, including specific mechanisms of dislocation propagation and annihilation, along with the evolution of specific dislocation populations through dislocation density analyses.

Keywords: dislocations, intermittent plasticity, molecular dynamics, slip distributions

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Authors: Quang Dong Dang

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This paper examines the possible effects of stock market developments by channels on income and wealth inequality. We use the Bayesian Multilevel Model with the explanatory variables of the market’s channels, such as accessibility, efficiency, and market health in six selected countries: the US, UK, Japan, Vietnam, Thailand, and Malaysia. We found that generally, the improvements in the stock market alleviate income inequality. However, stock market expansions in higher-income countries are likely to trigger income inequality. We also found that while enhancing the quality of channels of the stock market has counter-effects on wealth equality distributions, open accessibilities help reduce wealth inequality distributions within the scope of the study. In addition, the inverted U-shaped hypothesis seems not to be valid in six selected countries between the period from 2006 to 2020.

Keywords: Bayesian multilevel model, income inequality, inverted u-shaped hypothesis, stock market development, wealth inequality

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Authors: David C. Ni

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In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Changshan Zhang, Zhijin Yu, Shixing Fan

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A comprehensive hazard evaluation for coal self-heating in composite long-wall gobs is heavily dependent on computational simulation. In this study, the spatial distributions of cracks which caused significant air leakage were simulated by universal distinct element code (UDEC) simulation. Based on the main routes of air leakage and characteristics of coal self-heating, a computational fluid dynamics (CFD) modeling was conducted to model the coal spontaneous combustion dangerous area in composite long-wall gobs. The results included the oxygen concentration distributions and temperature profiles showed that the numerical approach is validated by comparison with the test data. Furthermore, under the conditions of specific engineering, the major locations where some techniques for extinguishing and preventing long-wall gob fires need to be put into practice were also examined.

Keywords: computational simulation, UDEC simulation, coal self-heating, CFD modeling, long-wall gobs

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Authors: Ebissa Gadissa Kedir, C. S. P. Ojha, K. S. Hari Prasad

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In the present study, the depth-averaged velocity and boundary shear stress in non-prismatic compound channels with three different converging floodplain angles ranging from 1.43ᶱ to 7.59ᶱ have been studied. The analytical solutions were derived by considering acting forces on the channel beds and walls. In the present study, five key parameters, i.e., non-dimensional coefficient, secondary flow term, secondary flow coefficient, friction factor, and dimensionless eddy viscosity, were considered and discussed. An expression for non-dimensional coefficient and integration constants was derived based on the boundary conditions. The model was applied to different data sets of the present experiments and experiments from other sources, respectively, to examine and analyse the influence of floodplain converging angles on depth-averaged velocity and boundary shear stress distributions. The results show that the non-dimensional parameter plays important in portraying the variation of depth-averaged velocity and boundary shear stress distributions with different floodplain converging angles. Thus, the variation of the non-dimensional coefficient needs attention since it affects the secondary flow term and secondary flow coefficient in both the main channel and floodplains. The analysis shows that the depth-averaged velocities are sensitive to a shear stress-dependent model parameter non-dimensional coefficient, and the analytical solutions are well agreed with experimental data when five parameters are included. It is inferred that the developed model may facilitate the interest of others in complex flow modeling.

Keywords: depth-average velocity, converging floodplain angles, non-dimensional coefficient, non-prismatic compound channels

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Authors: Bawadi M. A., Abbad J. A., Baras E. A.

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This study was conducted to assess wind energy resources in the area of Al-Adwas Ras-Huwirah Hadhramout Governorate, Yemen, through using statistical calculations, the Weibull model and SPSS program were used in the monthly and the annual to analyze the wind energy resource; the convergence of wind energy; turbine efficiency in the selected area. Wind speed data was obtained from NASA over a period of ten years (2010-2019) and at heights of 50 m above ground level. Probability distributions derived from wind data and their distribution parameters are determined. The density probability function is fitted to the measured probability distributions on an annual basis. This study also involves locating preliminary sites for wind farms using Geographic Information System (GIS) technology. This further leads to maximizing the output energy from the most suitable wind turbines in the proposed site.

Keywords: wind speed analysis, Yemen wind energy, wind power density, Weibull distribution model

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Authors: Ranjan Banerjee, W. D. Gunawardana

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The free vibration and flutter analysis plays a major part in aircraft design which is indeed, a mandatory requirement. In particular, high aspect ratio transport airliner wings are prone to free vibration and flutter problems that must be addressed during the design process as demanded by the airworthiness authorities. The purpose of this paper is to carry out a detailed free vibration and flutter analysis for a wide range of high aspect ratio aircraft wings and generate design curves to provide useful visions and understandings of aircraft design from an aeroelastic perspective. In the initial stage of the investigation, the bending and torsional stiffnesses of a number of transport aircraft wings are looked at and critically examined to see whether it is possible to express the stiffness distributions in polynomial form, but in a sufficiently accurate manner. A similar attempt is made for mass and mass moment of inertia distributions of the wing. Once the choice of stiffness and mass distributions in polynomial form is made, the high aspect ratio wing is idealised by a series of bending-torsion coupled beams from a structural standpoint. Then the dynamic stiffness method is applied to compute the natural frequencies and mode shape of the wing. Next the wing is idealised aerodynamically and to this end, unsteady aerodynamic of Theodorsen type is employed to represent the harmonically oscillating wing. Following this step, a normal mode method through the use of generalised coordinates is applied to formulate the flutter problem. In essence, the generalised mass, stiffness and aerodynamic matrices are combined to obtain the flutter matrix which is subsequently solved in the complex domain to determine the flutter speed and flutter frequency. In the final stage of the investigation, an exhaustive parametric study is carried out by varying significant wing parameters to generate design curves which help to predict the free vibration and flutter behaviour of high aspect ratio transport aircraft wings in a generic manner. It is in the aeroelastic context of aircraft design where the results are expected to be most useful.

Keywords: high-aspect ratio wing, flutter, dynamic stiffness method, free vibration, aeroelasticity

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Olawale Babatunde Olatinsu, Deborah Oluwaseun Olorode

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Industrial rocks were collected from a quarry site at Ewekoro in south-western Nigeria and analysed using Nuclear Magnetic Resonance (NMR) technique. NMR measurement was conducted on the samples in partial water-saturated and full brine-saturated conditions. Raw NMR data were analysed with the aid of T2 curves and T2 spectra generated by inversion of raw NMR data using conventional regularized least-squares inversion routine. Results show that NMR transverse relaxation (T2) signatures fairly adequately distinguish between the rock types. Similar T2 curve trend and rates at partial saturation suggests that the relaxation is mainly due to adsorption of water on micropores of similar sizes while T2 curves at full saturation depict relaxation decay rate as: 1/T2(shale)>1/ T2(glauconite)>1/ T2(limestone) and 1/T2(sandstone). NMR T2 distributions at full brine-saturation show: unimodal distribution in shale; bimodal distribution in sandstone and glauconite; and trimodal distribution in limestone. Full saturation T2 distributions revealed the presence of well-developed and more abundant micropores in all the samples with T2 in the range, 402-504 μs. Mesopores with amplitudes much lower than those of micropores are present in limestone, sandstone and glauconite with T2 range: 8.45-26.10 ms, 6.02-10.55 ms, and 9.45-13.26 ms respectively. Very low amplitude macropores of T2 values, 90.26-312.16 ms, are only recognizable in limestone samples. Samples with multiple peaks showed well-connected pore systems with sandstone having the highest degree of connectivity. The difference in T2 curves and distributions for the rocks at full saturation can be utilised as a potent diagnostic tool for discrimination of these rock types found at Ewekoro.

Keywords: Ewekoro, NMR techniques, industrial rocks, characterization, relaxation

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Authors: Ishapathik Das, Sumen Sen, N. Rao Chaganty, Pooja Sengupta

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Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models.

Keywords: copula, Gaussian copula, multivariate distributions, inflated distributios

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Authors: Sayed A. Elsayed, Emad Z. Ibrahim, Osama M. Mesalhy, Mohamed A. Abdelatief

Abstract:

An experimental and numerical study has been conducted to clarify fluid flow characteristics and pressure drop distributions of a cross-flow heat exchanger employing staggered wing-shaped tubes at different angels of attack. The water-side Rew and the air-side Rea were at 5 x 102 and at from 1.8 x 103 to 9.7 x 103, respectively. Three cases of the tubes arrangements with various angles of attack, row angles of attack and 90° cone angles were employed at the considered Rea range. Correlation of pressure drop coefficient Pdc in terms of Rea, design parameters for the studied cases were presented. The flow pattern around the staggered wing-shaped tubes bundle were predicted by using commercial CFD FLUENT 6.3.26 software package. Results indicated that the values of Pdc were increased by increasing the angle of attack from 0° to 45°, while the opposite was true for angles of attack from 135° to 180°. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.

Keywords: wing-shaped tubes, cross-flow cooling, staggered arrangement, CFD

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