interpolation of precipitation under topographic influence at different time scales 1 in this paper new methodologies for interpolating rainfall data in individual time intervals ranging from a day to a year using gaussian copulas and unsymmetrical v copulas with a variety of treatments of altitude as an exogenous variable are described for shorter time aggregations zeros were treated as censored variables for each selected time step the marginal distributions of precipitation amounts were modeled using nonparametric density estimators while the spatial dependence structures were estimated using a maximum likelihood methodology the methodology was compared to other common geostatistical interpolators such as ordinary kriging and external drift kriging several measures of bias and error structure have been used to assess the efficacy of the methods in a range of comparative split sampling studies the data set chosen for the study comprises daily precipitation time series over 41 years in three regions in germany measured at more than 1200 locations over a large area 126 144 km2 among the many findings in the paper the ones that stand out are i correlation between precipitation and topography increases with the length of time interval and is significantly improved by directional smoothing of topography ii the copula methods are superior to kriging methods in terms of quality of interpolation bias and uncertainty estimation iii the treatment of zeros as censored variables improves interpolation quality for daily and pentad values monthly and annual data in this region present no dry periods iv the copula methods yield full conditional distributions of estimates at a target point in an interval improving substantially on the simple uncertainty estimates derived from kriging and v the gauss copula in particular performs best overall in terms of computational efficiency combined with useful error profiles in the interpolations and of all methods is the most realistic in its error estimates

stochastic reconstruction and interpolation of precipitation fields using combined information of commercial microwave links and rain gauges for the reconstruction and interpolation of precipitation fields we present the application of a stochastic approach called random mixing generated fields are based on a data set consisting of rain gauge observations and path averaged rain rates estimated using commercial microwave link cml derived information precipitation fields are received as linear combination of unconditional spatial random fields where the spatial dependence structure is described by copulas the weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced the innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size each ensemble member is in concordance with the observed path averaged cml derived rain rates and additionally reflects the observed rainfall variability along the cml paths the ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields the method is demonstrated both for a synthetic data set and a real world data set in south germany while the synthetic example allows an evaluation against a known reference the second example demonstrates the applicability for real world observations generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality a performance evaluation of random mixing compared to ordinary kriging demonstrates an improvement of the reconstruction of the observed spatial variability random mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them in particular when different measurement types are combined

copula based geostatistical models for groundwater quality parameters 1 groundwater quality parameters exhibit considerable spatial variability geostatistical methods including the assessment of variograms are usually used to characterize this variability copulas offer an interesting opportunity to describe dependence structures for multivariate distributions bivariate empirical copulas can be used as an alternative to variograms and covariance functions for the description of the spatial variability rank correlations of these copulas express the strength of the dependence independently of the marginal distributions and thus offer an alternative to the variograms empirical copulas for four quality parameters chloride sulfate ph and nitrate obtained from a large scale groundwater quality measurement network in baden wurttemberg germany are calculated they indicate that the spatial dependence structure of the investigated parameters is not gaussian two theoretical copula based models are presented in this paper a gaussian and a non gaussian bootstrap based statistical tests using stochastic simulation of the multivariate distributions are used to investigate the appropriateness of the models according to the test results the gaussian copula is rejected for most of the parameters while the non gaussian alternative is not rejected in most cases

robust stabilization of interval plants using lead or lag compensators abstract a lead or lag compensator robustly stabilizes a family of interval plants if and only if it simultaneously stabilizes the vertex plants

copula based daily rainfall disaggregation model 1 a daily rainfall disaggregation model which uses a copula to model the dependence structure between total depth total duration of wet periods and the maximum proportional depth of a wet period is presented the wet 1 dry 0 binary sequence is modeled by the nonrandomized bartlett lewis model with diurnal effect incorporated before superimposing the ar 1 depth process submodel unlike previous studies the model is structured such that all wet day data available are considered in the analysis without the need to discard any good quality daily data embedded in a month having some missing data this increased the data size thus improving the modeling process further the daily data are classified according to the total duration of wet periods duration within the day in this way a large proportion of the model parameters become seasonal invariant the overriding factor being the total duration of wet periods the potential of the developed model has been demonstrated by disaggregating both the data set used in developing the model parameters and also a 12 year continuous rainfall data set not used in the model parameterization gross rainfall statistics of several aggregation levels down to 6 min have been very well reproduced by the disaggregation model the copula dependence structure and the variation of the depth process submodel parameters with the total duration of wet periods are also very well captured by the presented model

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

multivariate copula analysis toolbox mvcat describing dependence and underlying uncertainty using a bayesian framework we present a newly developed multivariate copula analysis toolbox mvcat which includes a wide range of copula families with different levels of complexity mvcat employs a bayesian framework with a residual based gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties the contribution of this paper is threefold a providing a bayesian framework to approximate the predictive uncertainties of fitted copulas b introducing a hybrid evolution markov chain monte carlo mcmc approach designed for numerical estimation of the posterior distribution of copula parameters and c enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties we show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima the proposed method however addresses this limitation and improves describing the dependence structure mvcat also enables evaluation of uncertainties relative to the length of record which is fundamental to a wide range of applications such as multivariate frequency analysis

principles of multivariate analysis a user s perspective part i looking at multivariate data part ii samples populations and models part iii analysing ungrouped data part iv analysing grouped data part v analysing association among variables appendix some basic matrix theory a1 definitions a2 elementary arithmetic operations a3 determinants and inverses a4 quadratic forms a5 latent roots and vectors a6 matrix square root a7 partitioned matrices a8 vector differentiation references index

improved spatial prediction a combinatorial approach 1 this paper presents a combinatorial approach for improving spatial predictions first copulas are used to interpolate a spatially distributed point rainfall field to a uniform spatial grid it is observed that results vary substantially depending on the parameters chosen for interpolation leading to the hypothesis that it may be advantageous to estimate copula parameters locally or to combine local and global copula predictions it is found that by modifying the method of forecast combinations prediction errors in the spatial interpolation of rainfall can be reduced although this method of combining predictions is applied in the context of rainfall interpolation using local and global copula predictions it can be used on other spatial variables and interpolation methods

input impedance of a probe fed stacked circular microstrip antenna the input impedance of a microstrip antenna consisting of two circular microstrip disks in a stacked configuration driven by a coaxial probe is investigated a rigorous analysis is performed using a dyadic green s function formulation whereby the mixed boundary value problem is reduced to a set of coupled vector integral equations using the vector hankel transform galerkin s method is used in the spectral domain using two sets of disk current expansions one set is based on the complete set of orthogonal modes of the magnetic cavity and the other uses chebyshev polynomials with the proper edge condition for the disk currents an additional term is added to the disk current expansion to model the current properly in the vicinity of the probe disk junction the input impedance of the antenna including the probe self impedance is calculated as a function of the layered parameters and the ratio of the two disk radii disk current distributions and radiation patterns are presented the calculated results are shown to be in good agreement with experimental data

on nonparametric measures of dependence for random variables in 1959 a renyi proposed a set of axioms for a measure of dependence for pairs of random variables in the same year a sklar introduced the general notion of a copula this is a function which links an n dimensional distribution function to its one dimensional margins and is itself a continuous distribution function on the unit n cube with uniform margins we show that the copula of a pair of random variables x y is invariant under a s strictly increasing transformations of x and y and that any property of the joint distribution function of x and y which is invariant under such transformations is solely a function of their copula exploiting these facts we use copulas to define several natural nonparametric measures of dependence for pairs of random variables we show that these measures satisfy reasonable modifications of renyi s conditions and compare them to various known measures of dependence e g the correlation coefficient and spearman s rho

extreme point results for robust stabilization of interval plants with first order compensators it has been shown previously that a first order compensator robustly stabilizes an internal plant family if and only if it stabilizes all of the extreme plants these extreme plants are obtained by considering all possible combinations for the extreme values of the numerator and denominator coefficients in this work the authors prove a stronger result namely that it is necessary and sufficient to stabilize only sixteen of the extreme plants these sixteen plants are generated using the kharitonov polynomials associated with the numerator and denominator furthermore when additional information about the compensator is specified sign of the gain and signs and relative magnitudes of the pole and zero then in some cases it is necessary and sufficient to stabilize eight critical plants while in other cases it is necessary and sufficient to stabilize twelve critical plants

two site modeling of rainfall based on the neyman scott process on the basis of the neyman scott process a model is proposed to generate rainfall at two sites simultaneously this model takes into account the correlation which is produced by generating bivariate correlated variates the cross correlation between the sites has been computed in order to estimate the parameters finally the model is validated for three pairs of stations situated in the swiss plateau region

streamflow prediction in ungauged catchments using copula based dissimilarity measures 1 there are many procedures in the available literature to perform prediction in ungauged basins commonly the euclidean metric is used as a proxy of the hydrologic dissimilarity here we propose a procedure to find a metric on the basis of dissimilarity measures that are estimated from pairwise empirical copula densities of runoff a metric is then defined in an transformed space of basin descriptors whose parameterization is obtained with a variance reducing technique a hydrologic model was run in an ungauged basin with sets of global parameters obtained from the k nearest neighboring donor basins using various metrics to take into account the uncertainty of its parameterization hydrologic model parameters were regionalized with a multiscale parameter regionalization technique whose transfer function parameters were found via calibration the streamflow in an ungauged basin was found as an ensemble streamflow prediction to account for the uncertainties of the transfer function parameters as well as those to define the metric this technique was applied in 38 german basins ranging in size from 70 to 4000 km2 for each basin a number of catchment descriptors and several climatic indices were quantified e g mean slope aspect shape factor mean elevation and mean monthly temperature in january among others daily streamflow time series correspond to the period from 1961 to 2000 simulated daily discharge was validated with a jackknife cross validation technique nash sutcliffe efficiencies obtained in this way ranged between 0 76 and 0 86 these results suggested that the proposed technique would produce reasonable results in ungauged basins

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

a spatial markov model for the evolution of the joint distribution of groundwater age arrival time and velocity in heterogeneous media the evolution of the joint distribution of groundwater age velocity and arrival times based on a markov model for the velocities of fluid particles in heterogeneous porous media has been quantified an explicit evolution equation for the joint distribution of age arrival time and particle velocity is derived which is equivalent to a continuous time random walk for age velocity and arrival time the approach is fully parameterized by the correlation model and the distribution of groundwater flow velocities the transition probability for subsequent particle velocities along streamlines is implemented by a copula which is an efficient method to generate a correlated velocity series with prescribed marginal distribution we discuss different solution methods based on finite differences and random walk particle tracking the latter is based on continuous time random walks whose transition times are obtained kinematically from the flow velocities specifically we discuss a renormalization scheme to accelerate the particle tracking simulations based on the definition of aggregate particle transitions while at the same time renormalizing velocity correlation the impact of velocity correlation and velocity distribution on the evolution of age at different distances from the inlet plane is also studied at distances of the order of the correlation length persistent particle velocities give the same behavior as stochastic streamtube models for velocity distributions which give rise to transition times with finite variance the age distributions evolve toward an inverse gaussian for heavy tailed weighting times they evolve toward stable distribution as the distance from the inlet increases

geostatistical interpolation using copulas 1 in many applications of geostatistical methods the dependence structure of the investigated parameter is described solely with the variogram or covariance functions which are susceptible to measurement anomalies and implies the assumption of gaussian dependence moreover the kriging variance respects only observation density data geometry and the variogram model to address these problems we borrow the idea from copulas to depict the dependence structure without the influence of the marginal distribution the methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the gaussian copula as well as a non gaussian copula are used in this paper copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function the interpolation is carried out with two different copulas where the expected and median values are calculated from the copulas conditioned with the nearby observations the full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values observations of a large scale groundwater quality measurement network in baden wurttemberg are used to demonstrate the methodology five groundwater quality parameters chloride nitrate ph sulfate and dissolved oxygen are investigated all five parameters show non gaussian dependence the copula based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging different statistical measures including mean squared error relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods the non gaussian copulas give better results than the geostatistical interpolations validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging

bivariate frequency analysis of floods using a diffusion based kernel density estimator recent focus of flood frequency analysis ffa studies has been on development of methods to model joint distributions of variables such as peak flow volume and duration that characterize a flood event as comprehensive knowledge of flood event is often necessary in hydrological applications diffusion process based adaptive kernel d kernel is suggested in this paper for this purpose it is data driven flexible and unlike most kernel density estimators always yields a bona fide probability density function it overcomes shortcomings associated with the use of conventional kernel density estimators in ffa such as boundary leakage problem and normal reference rule the potential of the d kernel is demonstrated by application to synthetic samples of various sizes drawn from known unimodal and bimodal populations and five typical peak flow records from different parts of the world it is shown to be effective when compared to conventional gaussian kernel and the best of seven commonly used copulas gumbel hougaard frank clayton joe normal plackett and student s t in estimating joint distribution of peak flow characteristics and extrapolating beyond historical maxima selection of optimum number of bins is found to be critical in modeling with d kernel

modeling complex geological structures with elementary training images and transform invariant distances 1 we present a new framework for multiple point simulation involving small and simple training images the use of transform invariant distances by applying random transformations expands the range of structures available in the simple patterns of the training image the training image is no longer regarded as a global conceptual geological model but rather a basic structural element of the subsurface complex geological structures are obtained whose spatial structure can be parameterized by adjusting the statistics of the random transformations on the basis of field data or geological context in most cases such parameterization is possible by adjusting two numbers only this method allows us to build models that 1 reproduce shapes corresponding to a desired prior geological concept and 2 are in phase with different types of field observations such as orientation hydrofacies or geophysical measurements the main advantage is that the training images are so simple that they can be easily built even in 3 d we apply the method on a synthetic example involving seismic data where the transformation parameters are data driven we also show examples where realistic 2 and 3 d structures are built from simplistic training images with transformation parameters inferred using a small number of orientation data

joint probability of precipitation and discharge deficits in the netherlands 1 the netherlands are situated at the downstream end of the rhine river a large part of the country can be supplied with water from the river in the case of precipitation deficits for drought assessment it is therefore necessary to consider the joint distribution of precipitation and discharge deficits a transformed bivariate normal distribution as well as a bivariate gumbel distribution are fitted to this data in addition nearest neighbor resampling is used to estimate joint probabilities of precipitation and discharge deficits both the reproduction of the marginal distributions and the dependence structure are explored it is found that the transformed bivariate normal distribution underestimates the probability that both the precipitation and discharge deficit are extreme due to its asymptotic independence nearest neighbor resampling also underestimates this probability mainly because the upper tails of the marginal distributions are not properly reproduced by the simulations from the two fitted bivariate distributions a novel bivariate distribution is constructed with transformed normal marginals and a logistic gumbel dependence structure which gives the best description of the upper tail of the joint distribution the use of a failure region based on economic damage rather than on joint exceedances considerably reduces the differences between the probabilities of drought from the various bivariate models

entropy copula method for single site monthly streamflow simulation 1 an entropy copula method is proposed for single site monthly streamflow simulation in this method the joint distribution of adjacent monthly streamflows is constructed using the copula method whereas the marginal distribution of streamflow for each month is derived using the entropy method then the conditional distribution is derived from which monthly streamflow is generated moment statistics of monthly streamflow such as mean standard deviation and skewness can be modeled by the entropy based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula based joint distribution the proposed entropy copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence application to the simulation of monthly streamflow from the colorado river illustrates the effectiveness of the proposed method

a generalization of kharitonov s theorem robust stability of interval plants the robust stability problem is considered for interval plants in the case of single input multioutput or single output multi input systems a necessary and sufficient condition for the robust stabilization of such plants is developed using a generalization of v l kharitonov s theorem 1978 the generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta s q sub 1 s p sub 1 s q sub m s p sub m s where the q sub i are fixed and the p sub i are interval polynomials the coefficients of which are regarded as a point in parameter space which varies within a prescribed box this generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments it is shown that for special classes of polynomials q sub i s the set of line segments collapses to a set of points and this version of the box theorem in turn reduces to kharitonov s original theorem

bivariate extreme value distributions an application of the gibbs sampler to the analysis of floods the quantitative definition of the magnitude of a flood episode exclusively in terms of its peak rate of discharge is often insufficient in common with most episodic hydrological phenomena floods are intrinsically multivariate random events characterized not only by their peak flow but also by their volume and the duration of discharge above critical thresholds a complete definition in terms of these three component random variables has not found its way into standard analytical practice this may be partly because the theory of multivariate extremes is not straightforward and partly because no intuitively attractive way of presenting the component variables in a probabilistic framework has been put forward we propose that the gibbs sampler a member of the new generation of computer intensive methods in computational statistics bypasses the theoretical difficulties we demonstrate the gibbs sampler and provide graphical presentations of the results for the annual flood hydrograph on the mekong river at vientiane laos we extend the results to evaluate the potential distribution of flood damage to the city

fdtd calculation of wide band antenna gain and efficiency absolute gain and radiation efficiency are calculated using the finite difference time domain fdtd method the method described utilizes pulsed excitation so that wideband results are available from a single fdtd computation the approach is demonstrated for a simple wire antenna geometry and is validated by comparison with results obtained using the method of moments

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

frequency analysis via copulas theoretical aspects and applications to hydrological events 1 in this paper we provide a general theoretical framework exploiting copulas for studying the return periods of hydrological events in particular we consider events depending upon the joint behavior of two nonindependent random variables an approach which can easily be generalized to the multivariate case we show that using copulas may greatly simplify the calculations and may even yield analytical expressions for the isolines of the return periods both in the unconditional and in the conditional case in addition we show how a new probability distribution may be associated with the return period of specific events and introduce the definitions of sub super and critical events as well as those of primary and secondary return periods an illustration of the techniques proposed is provided by analyzing some case studies already examined in literature

analytical relationship between gaussian and transformed gaussian spatially distributed fields 1 a transformation of a gaussian random field results in a change of the spatial dependence in simple terms the range and the shape of a variogram are different between an underlying gaussian and a transformed gaussian field there is a relationship between the underlying and the transformed spatial dependence this paper shows how this relationship can be expressed analytically rather than generating multidimensional random fields and conducting spatial statistical analysis we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non gaussian random fields for any type of geostatistical parameterization such a mapping can also yield accurate estimation of the spatial correlation of the underlying gaussian field given the spatial correlation of the transformed field results indicate that 1 a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure and 2 the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically and it is sufficient to do this in one dimension we use the developed approach to investigate the change of correlations of connected random fields generated by the absolute value transformation results show 1 the correlation lengths of the underlying gaussian fields are 1 67 and 2 64 times of those of transformed non gaussian fields for gaussian and exponential covariance models respectively 2 the anisotropic ratio does not change and 3 the anticorrelation in hole effect correlation models disappear

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

brief condition and algorithm for simultaneous stabilization of linear plants this paper is devoted to the problem of simultaneous stabilization of linear plants it is shown that four given plants p i s i 1 2 3 4 are simultaneously stabilizable if and only if there exist four stable polynomials h i s i 1 2 3 4 which simultaneously satisfy two polynomial equations if we can only find four stable h i s i 1 2 3 4 to satisfy one of the two polynomial equations then two controllers c 1 s and c 2 s having a common denominator or numerator can be obtained such that c 1 s simultaneously stabilizes p 1 s and p 3 s and c 2 s simultaneously stabilizes p 2 s and p 4 s which is called the simultaneous stabilization in groups based on such two controllers a design algorithm for the simultaneous stabilization of three plants is induced

gaussian and non gaussian inverse modeling of groundwater flow using copulas and random mixing this paper presents a new copula based methodology for gaussian and non gaussian inverse modeling of groundwater flow the presented approach is embedded in a monte carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function the target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields the corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability and honors all the observations of hydraulic transmissivities the constraints related to hydraulic head observations are nonlinear in order to fulfill these constraints a connected domain in the weight space inside which all linear constraints are fulfilled is identified this domain is defined analytically and includes an infinite number of conditional fields i e conditioned on the observed hydraulic transmissivities and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads this procedure enables the simulation of a great number of solutions for the inverse problem allowing a reasonable quantification of the associated uncertainties the methodology can be used for fields with gaussian copula dependence and fields with specific non gaussian copula dependence further arbitrary marginal distributions can be considered

extreme point results for robust stability of interval plants beyond first order compensators motivated by robust stabilization of interval plants this paper concentrates on a fundamental problem involving a family of polynomials obtained via convex combination of extreme members the objective is to provide conditions under which stability of the extremes implies stability of the entire family although the existing literature contains rather strong extreme point results involving frequency domain analysis there is a paucity of more direct coefficient space criteria this paper deals exclusively with the coefficient space problem to this end we introduce the so called alternating hurwitz minor condition ahmc and show how it can be used to enlarge the class of polynomial families for which extreme point results can be obtained subsequently the ramifications on robust stability of interval plants are fully explained in contrast to existing literature for first order compensators the ahmc makes it possible to deal with classes of higher order compensators in an extreme point context

analysis of microstrip patch antennas using finite difference time domain method the study of microstrip patch antennas is directly treated in the time domain using a modified finite difference time domain fdtd method assuming an appropriate choice of excitation the frequency dependence of the relevant parameters can readily be found using the fourier transform of the transient current the fdtd method allows a rigorous treatment of one or several dielectric interfaces different types of excitation can be taken into consideration coaxial microstrip lines etc plotting the spatial distribution of the current density gives information about the resonance modes the usual frequency dependent parameters input impedance radiation pattern are given for several examples

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

trivariate statistical analysis of extreme rainfall events via the plackett family of copulas 1 recent hydrologic studies on multivariate stochastic analysis have indicated that copulas perform well for bivariate problems in particular the frank family of archimedean copulas has been a popular choice for a dependence model however there are limitations to extending such archimedean copulas to trivariate and higher dimensions with very specific restrictions on the kinds of dependencies that can be modeled in this study we examine a non archimedean copula from the plackett family that is founded on the theory of constant cross product ratio it is shown that the plackett family not only performs well at the bivariate level but also allows a trivariate stochastic analysis where the lower level dependencies between variables can be fully preserved while allowing for specificity at the trivariate level as well the feasible range of plackett parameters that would result in valid 3 copulas is determined numerically the trivariate plackett family of copulas is then applied to the study of temporal distribution of extreme rainfall events for several stations in indiana where the estimated parameters lie in the feasible region on the basis of a given rainfall depth and duration conditional expectations of rainfall features such as expected peak intensity time to peak and percentage cumulative rainfall at 10 cumulative time increments are evaluated the results of this study suggest that while the constant cross product ratio theory was conventionally applied to discrete type random variables it is also applicable to continuous random variables and that it provides further flexibility for multivariate stochastic analyses of rainfall

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

bayesian assessment of the expected data impact on prediction confidence in optimal sampling design 1 incorporating hydro geo logical data such as head and tracer data into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty because of financial limitations for investigation campaigns information needs toward modeling or prediction goals should be satisfied efficiently and rationally optimal design techniques find the best one among a set of investigation strategies they optimize the expected impact of data on prediction confidence or related objectives prior to data collection we introduce a new optimal design method called predia gnosis preposterior data impact assessor predia derives the relevant probability distributions and measures of data utility within a fully bayesian generalized flexible and accurate framework it extends the bootstrap filter bf and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values predia is a strictly formal information processing scheme free of linearizations it works with arbitrary simulation tools provides full flexibility concerning measurement types linear nonlinear direct indirect allows for any desired task driven formulations and can account for various sources of uncertainty e g heterogeneity geostatistical assumptions boundary conditions measurement values model structure uncertainty a large class of model errors via bayesian geostatistics and model averaging existing methods fail to simultaneously provide these crucial advantages which our method buys at relatively higher computational costs we demonstrate the applicability and advantages of predia over conventional linearized methods in a synthetic example of subsurface transport in the example we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence hence predia will often lead to substantially better sampling designs finally we extend our example to specifically highlight the consideration of conceptual model uncertainty

stability conditions for polytopes of polynomials in considering the stability or performance of linear systems with uncertain parameters one is led to consider the simultaneous stability of families of polynomials for a general stability region in the complex plane the author gives a stability criterion for polytopes of polynomials in terms of the stability of a minimal number of corners and edges of the polytope the testing set of edges and corners depends entirely on the edge directions of the polytope hence the results are particularly applicable to problems with fixed directions but varying lengths and positions of the edges applications to robust pole placement of uncertain systems and computation of worst case h sub infinity norms are demonstrated

analysis of microstrip antennas on a curved surface using the conformal grids fd td method the need for small portable antennas for mobile communications has spurred the study of microstrip antennas msa msa are quite flexible and have been used as conformal antennas on arbitrary curved surfaces the characteristics of conformal msa can be expected to differ from those of planar models dependable numerical analyses will obviate many of the costs and other inconveniences associated with experiments but as antennas may be mounted on surfaces of arbitrary topological complexity analysis methods must have a general applicability the curvilinear finite difference time domain fd td method has shown excellent versatility this method is applied to analyze microstrip antennas mounted on curved surfaces the numerical predictions are compared with the experimental values the results confirm the predictions within acceptable limits and appear to confirm the validity of the method as a result it was confirmed that the input impedance and directivity of msa on curved surfaces are different from the flat msa

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

fitting bivariate copulas to the dependence structure between storm characteristics a detailed analysis based on 105 year 10 min rainfall 1 the use of copulas as flexible tools for constructing marginal free distribution functions for multivariate phenomena such as rainfall recently enjoys substantial attention by researchers in hydrology in this study commonly used bivariate copulas and techniques for fitting such bivariate copulas are applied to different couples of storm variables based on an extensive data set of 105 years of 10 min rainfall observed at uccle belgium in the analysis various problems that can occur are highlighted and opportunities for further research are outlined after selecting storms and introducing a meaningful solution to circumvent the presence of abundant ties in the data a detailed seasonal dependence analysis is provided together with a study on tail dependence further different existing parameter estimation techniques and goodness of fit methods for selecting the most appropriate bivariate copulas are applied and compared finally attention is given to the presence of asymmetric dependence and nonexchangeability

a comparative copula based bivariate frequency analysis of observed and simulated storm events a case study on bartlett lewis modeled rainfall 1 because of a lack of historical rainfall time series of considerable length one often has to rely on simulated rainfall time series e g in the design of hydraulic structures one way to simulate such time series is by means of stochastic point process rainfall models such as the bartlett lewis type of model for the evaluation of model performance with a focus on the reproduction of extreme rainfall events often a univariate extreme value analysis is performed recently developed concepts in statistical hydrology now offer other means of evaluating the overall performance of such models in this study a copula based frequency analysis of storms is proposed as a tool to evaluate differences between the return periods of several types of observed and modeled storms first this study performs an analysis of several storm variables which indicates a problem with the modeling of the temporal structure of rainfall by the models thereafter the bivariate frequency analysis of storms defined by their duration and volume illustrates the underestimation and overestimation of the return period of the storms simulated by the models which is partially explained by a large difference in the marginal distribution functions of the storm duration and storm volume the difference in the degree of association between the latter and a different mean storm interarrival time the proposed methodology allows for the identification of some problems with the rainfall simulations from which recommendations for possible improvements to rainfall models can be made

hurwitz testing sets for parallel polytopes of polynomials in considering robustness of linear systems with uncertain paramenters one is lead to consider simultaneous stability of families of polynomials efficient hurwitz stability tests for polytopes of polynomials have earlier been developed using evaluations on the imaginary axis this paper gives a stability criterion for parallel polytopes in terms of hurwitz stability of a number of corners and edges the testing set of edges and corners depends entirely on the edge directions of the polytope hence the results are particularly applicable in simultaneous analysis of several polytopes with equal edge directions it follows as a consequence that kharitonov s four polynomial test for independent coefficient uncertainties is replaced by a test of 2q polynomials when the stability region is a sector eiv 0 r q v and r q is a rational number

a family of distributions for modelling non elliptically symmetric multivariate data summary the paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation we present a relatively simple family of distributions for use in describing data which are not elliptically symmetric properties of the family are discussed and it is shown that multivariate pareto burr and logistic distributions are special cases in addition simulation methods for applications in monte carlo robustness studies are outlined and finally the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution

a new extension to kharitonov s theorem an extension to a well known theorem due to kharitonov is presented kharitonov s theorem gives a necessary and sufficient condition for all polynomials in a given family to be hurwitz stable in kharitonov s theorem the family of polynomials considered is obtained by allowing each of the polynomial coefficients to vary independently within an interval kharitonov s theorem shows that stability of this family of polynomials can be determined by looking at the stability of four specially constructed vertex polynomials kharitonov s theorem is extended to allow for more general families of polynomials and to allow a given margin of stability to be guaranteed for the family of polynomials

a class of weak kharitonov regions for robust stability of linear uncertain systems kharitonov s theorems are generalized to the problem of so called weak kharitonov regions for robust stability of linear uncertain systems given a polytope of characteristic polynomials p and a stability region d in the complex plane p is called d stable if the zeros of every polynomial in p are contained in d it is of interest to know whether the d stability of the vertices of p implies the d stability of p a simple approach is developed which unifies and generalizes many known results on this problem

a new rainfall model based on the neyman scott process using cubic copulas 1 a classical way to model rainfall is to use a poisson process authors generally employed cluster of rectangular pulses to reproduce the hierarchical structure of rainfall storms although independence between cell intensity and duration turned out to be a nonrealistic assumption only a few models link these variables in this paper a neyman scott cluster process considering dependence between cell depth and duration is developed we introduce this link with a cubic copula copulas are multivariate distributions modeling the dependence structure between variables preserving the marginal distributions thanks to this flexibility we are able to introduce a global concept of dependence between cell depth and duration we derive the aggregated moments first second and third order moments from the new model for several families of polynomial copulas and perform an application on belgium and american data