an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

mixing and relaxation dynamics of the henon map at the edge of chaos the mixing properties or sensitivity to initial conditions and relaxation dynamics of the henon map together with the connection between these concepts have been explored numerically at the edge of chaos it is found that the results are consistent with those coming from one dimensional dissipative maps this constitutes the first verification of the scenario in two dimensional cases and obviously reinforces the idea of weak mixing

asymmetric unimodal maps at the edge of chaos we numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x t 1 1 a x t z i i 1 2 correspond to x t 0 and x t 1 0 a or 2 t 0 1 2 at the edge of chaos we employ three distinct algorithms to characterize the power law sensitivity to initial conditions at the edge of chaos namely direct measure of the divergence of initially nearby trajectories the computation of the rate of increase of generalized non extensive entropies s q and multi fractal analysis the first two methods provide consistent estimates for the exponent governing the power law sensitivity in addition to this we verify that the multi fractal analysis does not provide precise estimates of the singularity spectrum f alpha especially near its extremal points such feature prevents to perform a fine check of the accuracy of the scaling relation between f alpha and the entropic index q thus restricting the applicability of the multi fractal analysis for studying the sensitivity to initial conditions in this class of asymmetric maps

two dimensional dissipative maps at chaos threshold sensitivity to initial conditions and relaxation dynamics abstract the sensitivity to initial conditions and relaxation dynamics of two dimensional maps are analyzed at the edge of chaos along the lines of nonextensive statistical mechanics we verify the dual nature of the entropic index for the henon map one q sen q rel w 1 related to its relaxation dynamics towards its stationary state attractor we also corroborate a scaling law between these two indices previously found for z logistic maps finally we perform a preliminary analysis of a linearized version of the henon map the smoothed lozi map we find that the sensitivity properties of all these z logistic henon and lozi maps are the same q sen 0 2445

an adaptive parameter tuning of particle swarm optimization algorithm an adaptive parameter tuning of particle swarm optimization based on velocity information apso vi algorithm is proposed in this paper the velocity convergence of particles is first analyzed and the relationship between the velocity of particle and the search failures is pointed out which reveals the reasons why pso has relative poor global searching ability then this algorithm introduces the velocity information which is defined as the average absolute value of velocity of all the particles a new strategy is presented that the inertia weight is dynamically adjusted according to average absolute value of velocity which follows a given nonlinear ideal velocity by feedback control which can avoid the velocity closed to zero at the early stage under the guide of the nonlinear ideal velocity apso vi can maintain appropriate swarm diversity and alleviate the premature convergence validly numerical experiments are conducted to compare the proposed algorithm with different variants of pso on some benchmark functions experimental results show that the proposed algorithm remarkably improves the ability of pso to jump out of the local optima and significantly enhance the convergence speed and precision

interval dynamic response analysis of vehicle bridge interaction system with uncertainty abstract interval dynamic response analysis of vehicle bridge interaction system with uncertain parameters is studied in this paper the bridge s and vehicle s parameters are considered as interval variables a half car model is used to represent a moving vehicle and the bridge is assumed as a simply supported euler bernoulli beam by introducing the interval algorithm into the dynamic analysis of vehicle bridge interaction system the expressions of the midpoint value interval width lower and upper bounds of interval bridge dynamic response are developed the lower and upper bounds are respectively the minimum and maximum values of bridge dynamic response which can also be determined by optimization approaches a heuristic optimization method a new particle swarm optimization method with low discrepancy sequence initialized particles and high order nonlinear time varying inertia weight and constant acceleration coefficients lhnpso is then developed to find the bounds of bridge displacement examples are used to illustrate the effectiveness of the presented methods and monte carlo simulations are implemented to validate the computational results the effects of individual system parameters on bridge response are also investigated

a bayesian nonparametric approach to reliability abstract it is suggested that problems in a reliability context may be handled by a bayesian non parametric approach a stochastic process is defined whose sample paths may be assumed to be either increasing hazard rates or decreasing hazard rates by properly choosing the parameter functions of the process the posterior distribution of the hazard rates are derived for both exact and censored data bayes estimates of hazard rates c d f s densities and means are found under squared error type loss functions some simulation is done and estimates graphed to better understand the estimators finally estimates of the c d f from some data in a paper by kaplan and meier are constructed author

estimating a survival curve when new is better than used let f be a distribution function on 0 and let s 1 f be its corresponding survival function f is new better than used nbu if sxsy sx y for all x and y let snx be the empirical survival function based on a random sample of size n from an nbu distribution function f this paper studies the estimator a nx defined as sup snx y sny where the supremum is taken over all y for which sny 0 we show that a n is an nbu survival curve and that it is strongly uniformly consistent for s when the underlying distribution has compact support for example when sampling is subject to type i censoring moreover in such problems we show that the rate of convergence of a n is optimal

tail ordering and asymptotic efficiency of rank tests on considere une relation d ordre partiel qui est entre la relation d ordre stochastique definie par lehmann 1955 et une relation d ordre associee a la propriete du rapport de vraisemblance monotone

inconsistency of the maximum likelihood estimator of a distribution having increasing failure rate average abstract marshall and proschan showed that the mle for a life distribution with increasing failure rate is strongly consistent ann math statist 1965 36 69 77 in this note the author shows that the mle for a life distribution with increasing failure rate average is not consistent in fact maximum likelihood estimation in the ifra case yields estimators of the average failure rate and of the distribution function which in general coverage a s to values other than the true values in the decreasing failure rate average case the mle fails to exist

mpso median oriented particle swarm optimization particle swarm optimization pso is a bio inspired optimization algorithm which has been empirically demonstrated to perform well on many optimization problems however it has two main weaknesses which have restricted the wider applications of pso the algorithm can easily get trapped in the local optima and has slow convergence speed therefore improvement and or elimination of these disadvantages are the most important objective in pso research in this paper we propose median oriented particle swarm optimization mpso to carry out a global search over entire search space with accelerating convergence speed and avoiding local optima the median position of particles and the worst and median fitness values of the swarm are incorporated in the standard pso to achieve the mentioned goals the proposed algorithm is evaluated on 20 unimodal multimodal rotated and shifted high dimensional benchmark functions and the results are compared with some well known pso algorithms in the literature the results show that mpso substantially enhances the performance of the pso paradigm in terms of convergence speed and finds global or good near global optimal in the functions

analysis and improvement of particle swarm optimization algorithm the effects of inertia weight on particle swarm optimization pso performance are analyzed a novel method of selecting inertia weight in pso is developed which can tune the expectations of inertia weights adaptively when the inertia weights are randomly selected and lead to effectively balance between the local and global search ability results of the two benchmark functions indicate that the pso algorithm based on the strategy of random inertia weight riw has been significantly improved on both optimization speed and computational accuracy

genls co evolutionary algorithm for nonlinear system of equations abstract in this paper we present a new optimization system genls for nonlinear system of equations our approach has two characteristic features firstly nonlinear system of equations is transformed into a nonlinear programming problem nlp with additional parameter e to define initial precision of the system that is the objective is to reduce the violation of the constraints to an acceptable level desired precision e by minimizing a function that measures the maximum violation of the constraints secondly efficient co evolutionary algorithm is implemented for solving the resulting nlp which combines concept of co evolution repairing procedure and elitist strategy finally we report numerical results in order to establish the actual computational burden of the proposed method and to assess its performances with respect to classical approaches for solving nonlinear system of equations

it cemop an iterative co evolutionary algorithm for multiobjective optimization problem with nonlinear constraints over the past few years researchers have developed a number of multiobjective evolutionary algorithms moeas although most studies concentrate on solving unconstrained optimization problems there exit a few studies where moeas have been extended to solve constrained optimization problems most of them were based on penalty functions for handling nonlinear constraints by genetic algorithms however the performance of these methods is highly problem dependent many methods require additional tuning of several parameters in this paper we present a new optimization algorithm which is based on concept of co evolution and repair algorithm for handling nonlinear constraints the algorithm maintains a finite sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of e dominance the use of e dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the pareto set approximation by choosing an appropriate e value which guarantees convergence and diversity the results provided by the proposed algorithm for six benchmark problems are promising when compared with exiting well known algorithms also our results suggest that our algorithm is better applicable for solving real world application problems

estimating the survival curve when new is better than used of a specified age abstract suppose that the survival function s of a random variable x is a member of the new better than used at age t 0 nbu t 0 class as defined by hollander park and proschan 1986 s must satisfy the condition s x t 0 s x s t 0 for all x 0 given a random sample from s an estimator is sought that itself belongs to the nbu t 0 class and has the same asymptotic optimality properties as the empirical survival curve s n the estimator s of s given implicitly by s x min s n x t 0 x t 0 when x t 0 with x s n x for x t 0 is studied a closed form representation for is derived is shown to be a strong uniformly consistent nbu t 0 estimator of s that converges to s at the best possible pointwise and mean squared rates the asymptotic distribution theory of is discussed and is derived explicitly for functions s for which s x t 0 s x s t 0 for all x 0 confidence procedures based on are discussed the final section describes the results of a simul

estimation of survival functions under uniform stochastic ordering abstract if s and t are survival functions for two life distributions then s is said to be uniformly stochastically smaller than t denoted by s t if x s x t x is nonincreasing in x on x t x 0 this ordering is transitive uniform stochastic ordering uso has found important applications in nonparametric accelerated life testing among other areas it has been shown that the nonparametric maximum likelihood estimator npmle of s under uso when t is known is inconsistent dykstra kochar robertson derived the restricted npmle s of several unknown survival functions linearly ordered by uso this article shows that these too are inconsistent in general rojo and samaniego gave excellent ad hoc estimators of s and t when the other is known based on their idea for the one sample problem they gave two ad hoc estimators one of them only implied of s and t when they are both unknown these are consistent but they lack some desirable properties this article introduces a one parameter famil

nonparametric goodness of fit tests for uniform stochastic ordering we propose lp distance based goodness of fit gof tests for uniform stochastic ordering with two continuous distributions f and g both of which are unknown our tests are motivated by the fact that when f and g are uniformly stochastically ordered the ordinal dominance curve r fg 1 is star shaped we derive asymptotic distributions and prove that our testing procedure has a unique least favorable configuration of f and g for p 1 we use simulation to assess finite sample performance and demonstrate that a modified one sample version of our procedure e g with g known is more powerful than the one sample gof test suggested by arcones and samaniego 2000 annals of statistics we also discuss sample size determination we illustrate our methods using data from a pharmacology study evaluating the effects of administering caffeine to prematurely born infants

a new method for solving a system of the nonlinear equations in this paper we use measure theory in the discrete case to solve a wide range of the nonlinear equations systems first by defining an error function we transform the problem to an optimal control problem in discrete case the new problem is modified into one consisting of the minimization of a linear functional over a set of radon measures the optimal measure then is approximated by a finite combination of atomic measures and the problem converted approximately to a finite dimensional nonlinear programming finally we obtain an approximate solution for the original problem furthermore we obtain the path from the initial point up to the approximate solution

on the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint we identify the asymptotic behavior of the estimators proposed by rojo and samaniego and mukerjee of a distribution f assumed to be uniformly stochastically smaller than a known baseline distribution g we show that these estimators are sqrt n convergent to a limit distribution with mean squared error smaller than or equal to the mean squared error of the empirical survival function by examining the mean squared error of the limit distribution we are able to identify the optimal estimator within mukerjee s class under a variety of different assumptions on f and g similar theoretical results are developed for the two sample problem where f and g are both unknown the asymptotic distribution theory is applied to obtain confidence bands for the survival function bar f based on published data from an accelerated life testing experiment

searching globally optimal parameter sequence for defeating runge phenomenon by immunity genetic algorithm data interpolation is a fundamental data processing tool in scientific studies and engineering applications however when interpolating data points on an equidistant grid using polynomials the so called runge phenomenon may occur making polynomial interpolation unreliable although there are some methods proposed to defeat the runge phenomenon it is still an open problem which parameter sequence is the globally optimal for overcoming the runge phenomenon in this paper we develop an immunity genetic algorithm based method to solve this problem specifically we first model the runge phenomenon defeating problem as an optimization in which the objective function is the energy of the parametric curve an immunity genetic algorithm is then devised to determine the best iga parameter sequence which minimizes the objective function the resulting parametric curve overcomes the runge phenomenon by performing the proposed immunity genetic searching algorithm starting with some groups of randomly generated parameter sequences the resulted parameter sequences closely oscillate around the chebyshev parameter sequence therefore the chebyshev parameter sequence is most likely the globally optimal sequence conquering the runge phenomenon

integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems heuristic optimization provides a robust and efficient approach for solving complex real world problems the aim of this paper is to introduce a hybrid approach combining two heuristic optimization techniques particle swarm optimization pso and genetic algorithms ga our approach integrates the merits of both ga and pso and it has two characteristic features firstly the algorithm is initialized by a set of random particles which travel through the search space during this travel an evolution of these particles is performed by integrating pso and ga secondly to restrict velocity of the particles and control it we introduce a modified constriction factor finally the results of various experimental studies using a suite of multimodal test functions taken from the literature have demonstrated the superiority of the proposed approach to finding the global optimal solution

consistent estimation of distributions with type ii bias with applications in competing risks problems a random variable x is symmetric about 0 if x and x have the same distribution there is a large literature on the estimation of a distribution function df under the symmetry restriction and tests for checking this symmetry assumption often the alternative describes some notion of skewness or one sided bias various notions can be described by an ordering of the distributions of x and x one such important ordering is that p 0 0 the distribution of x is said to have a type ii positive bias in this case if x has a density f then this corresponds to the density ordering f x f x for x 0 it is known that the nonparametric maximum likelihood estimator npmle of the df under this restriction is inconsistent we provide a projection type estimator that is similar to a consistent estimator of two dfs under uniform stochastic ordering where the npmle also fails to be consistent the weak convergence of the estimator has been derived which can be used for testing the null hypothesis of symmetry against this one sided alternative it also turns out that the same procedure can be used to estimate two cumulative incidence functions in a competing risks problem under the restriction that the cause specific hazard rates are ordered we also provide some real life examples

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

chaotic catfish particle swarm optimization for solving global numerical optimization problems abstract chaotic catfish particle swarm optimization c catfishpso is a novel optimization algorithm proposed in this paper c catfishpso introduces chaotic maps into catfish particle swarm optimization catfishpso which increase the search capability of catfishpso via the chaos approach simple catfishpso relies on the incorporation of catfish particles into particle swarm optimization pso the introduced catfish particles improve the performance of pso considerably unlike other ordinary particles the catfish particles initialize a new search from extreme points of the search space when the gbest fitness value global optimum at each iteration has not changed for a certain number of consecutive iterations this results in further opportunities of finding better solutions for the swarm by guiding the entire swarm to promising new regions of the search space and accelerating the search the introduced chaotic maps strengthen the solution quality of pso and catfishpso significantly the resulting improved pso and catfishpso are called chaotic pso c pso and chaotic catfishpso c catfishpso respectively pso c pso catfishpso c catfishpso as well as other advanced pso procedures from the literature were extensively compared on several benchmark test functions statistical analysis of the experimental results indicate that the performance of c catfishpso is better than the performance of pso c pso catfishpso and that c catfishpso is also superior to advanced pso methods from the literature

a solution to the optimal power flow using genetic algorithm optimal power flow opf is one of the main functions of power generation operation and control it determines the optimal setting of generating units it is therefore of great importance to solve this problem as quickly and accurately as possible this paper presents the solution of the opf using genetic algorithm technique this paper proposes a new methodology for solving opf this methodology is divided into two parts the first part employs the genetic algorithm ga to obtain a feasible solution subject to desired load convergence while the other part employs ga to obtain the optimal solution the main goal of this paper is to verify the viability of using genetic algorithm to solve the opf problem simultaneously composed by the load flow and the economic dispatch problem six buses system are used to highlight the goodness of this solution technique

measuring nonextensitivity parameters in a turbulent couette taylor flow we investigate probability density functions of velocity differences at different distances r measured in a couette taylor flow for a range of reynolds numbers re there is good agreement with the predictions of a theoretical model based on nonextensive statistical mechanics where the entropies are nonadditive for independent subsystems we extract the scale dependent nonextensitivity parameter q r mathrm re from the laboratory data

nonparametric estimation of a distribution subject to a stochastic precedence constraint for any two random variables x and y with distributions f and g defined on 0 x is said to stochastically precede y if p x y 1 2 for independent x and y stochastic precedence denoted by x spy is equivalent to e g x 1 2 the applicability of stochastic precedence in various statistical contexts including reliability modeling tests for distributional equality versus various alternatives and the relative performance of comparable tolerance bounds is discussed the problem of estimating the underlying distribution s of experimental data under the assumption that they obey a stochastic precedence sp constraint is treated in detail two estimation approaches one based on data shrinkage and the other involving data translation are used to construct estimators that conform to the sp constraint and each is shown to lead to a root n consistent estimator of the underlying distribution the asymptotic behavior of each of the estimators is fully characterized conditions are given under which

universal renormalization group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics we uncover the dynamics at the chaos threshold m of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period doubling cascade that occurs for m m we corroborate this structure analytically via the feigenbaum renormalization group rg transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential of which we determine the q index and the q generalized lyapunov coefficientl q our results are an unequivocal validation of the applicability of the nonextensive generalization of boltzmann gibbs statistical mechanics to critical points of nonlinear maps critical points of nonlinear maps offer a suitable playground for testing the validity of the nonextensive generalization of the boltzmann gibbs bg statistical mechanics proposed by tsallis over a decade ago 1 2 here we describe universal properties related to the dynamics of iterates at the onset of chaos in unimodal maps 3 which provide a literal confirmation of the generalized nonextensive theory to this end we employ the celebrated one dimensional logistic map f m x 512muxu 2 21 x 1 and the properties of its renormalization group rg fixed point to present evidence of previously unexposed scaling properties at the onset of chaos m5m at this state the most prominent of the map critical points the trajectories of the iterates exhibit an intricate structure that we describe and show is governed by the feigenbaum rg transformation 3 the domain of validity of bg statistical mechanics has been implicitly challenged by the proposal of its nonextensive generalization subsequent studies have offered experimental and numerical evidence that point out both the inadequacy of the standard bg statistics and the plausible competence of the generalized theory in describing various types of phenomena and systems this theoretical development represents an exceptional event in the long and trustworthy history of bg statistical mechanics however it is still in the process of being converted into a rigorously corroborated and fully understood fact the suggested circumstances under which the generalized theory is believed to be applicable at least with regards to nonlinear dynamical systems are those associated to a phase space with power law sensitivity to initial conditions to the consequent vanishing of the largest lyapunov exponent and to a fractal or multifractal geometrical structure 2 here we show that our results for the dynamics at the onset of chaos in unimodal maps constitute an unequivocal proof of the universal validity of the nonextensive statistics at such critical points in fact at the chaos threshold as well as at other critical points of the map the lyapunov exponent l 1 vanishes and the sensitivity to initial conditions j t for large iteration time t ceases to obey exponential behavior exhibiting instead a power law behavior 4 in order to describe the dynamics at such critical points the q exponential expression

a modified particle swarm optimizer with dynamic adaptation this paper proposes a modified particle swarm optimization algorithm with dynamic adaptation in this algorithm a modified velocity updating formula of the particle is used where the randomness in the course of updating particle velocity is relatively decreased and the inertia weight of each particle is different moreover this algorithm introduces two parameter describing the evolving state of the algorithm the evolution speed factor and aggregation degree factor by analyzing the influence of two parameters on the pso search ability a new strategy is presented that the inertia weight dynamically changes based on the run and evolution state in the strategy the inertia weight is given by a function of evolution speed factor and aggregation degree factor and the value of inertia weight is dynamically adjusted according to the evolution speed and aggregation degree the feature of the proposed algorithm is analyzed and several testing functions are performed in simulation study experimental results show that the proposed algorithm remarkably improves the ability of pso to jump out of the local optima and significantly enhance the convergence precision

two dimensional maps at the edge of chaos numerical results for the henon map the mixing properties or sensitivity to initial conditions of the two dimensional henon map have been explored numerically at the edge of chaos three independent methods which have been developed and used so far for one dimensional maps have been used to accomplish this task these methods are i the measure of the divergence of initially nearby orbits ii analysis of the multifractal spectrum and iii computation of nonextensive entropy increase rates the results obtained closely agree with those of the one dimensional cases and constitute a verification of this scenario in two dimensional maps this obviously makes the idea of weak chaos even more robust

estimation of a monotone mean residual life in survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age xmx defined by mx ex xx x where x is a lifetime m is called the mean residual life function in many applications it is reasonable to assume that m is decreasing dmrl or in creasing imrl we write decreasing increasing for nonincreasing non decreasing there is some literature on empirical estimators of m and their properties although tests for a monotone m are discussed in the literature we are not aware of any estimators of m under these order restrictions in this paper we initiate a study of such estimation our pro jection type estimators are shown to be strongly uniformly consistent on compact intervals and they are shown to be asymptotically root n equiv alent in probability to the unrestricted empirical estimator when m is strictly monotone thus the monotonicity is obtained free of charge at least in the aymptoticsense we also c onsider the nonparametricmaxi mum likelihood estimators they do not exist for the imrl case they do exist for the dmrl case but we have found the solutions to be too complex to be evaluated efficiently

pdf of velocity fluctuation in turbulence by a statistics based on generalized entropy an analytical formula for the probability density function pdf of the velocity fluctuation in fully developed turbulence is derived non perturbatively by assuming that its underlying statistics is the one based on the generalized measures of entropy the renyi entropy or the tsallis entropy the parameters appearing in the pdf including the index q in the generalized measures are determined self consistently with the help of the observed value of the intermittency exponent the derived pdf explains quite well the experimentally observed density functions

convergence to the critical attractor of dissipative maps log periodic oscillations fractality and nonextensivity for a family of logisticlike maps we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space we found that the phase space volume occupied by the ensemble w t depicts a power law decay with log periodic oscillations reflecting the multifractal character of the critical attractor we explore the parametric dependence of the power law exponent and the amplitude of the log periodic oscillations with the attractor s fractal dimension governed by the inflection of the map near its extremal point further we investigate the temporal evolution of w t for the circle map whose critical attractor is dense in this case we found w t to exhibit a rich pattern with a slow logarithmic decay of the lower bounds these results are discussed in the context of nonextensive tsallis entropies

on estimating a survival curve subject to a uniform stochastic ordering constraint abstract if f and g are cumulative distribution functions on 0 governing the lifetimes of specific systems under study and if f and g are their corresponding survival functions then f is said to be uniformly stochastically smaller than g denoted by f 0 when f and g are absolutely continuous f g is equivalent to the assumption that the corresponding failure rates are ordered the applicability of the notion of uniform stochastic ordering in reliability and life testing is discussed given that a random sample x 1 x n of lifetimes has been obtained from f where f is assumed to satisfy the uniform stochastic ordering constraint f g where g is fixed and known the problem of estimating f is addressed it has been shown elsewhere that the method of nonparametric maximum likelihood estimation fails to provide consistent estimators in this type of

statistical inference for uniform stochastic ordering in several populations tion for k population problems under uniform stochastic ordering restrictions we derive closed form estimates even with right censored data by a reparameterization which reduces the problem to a well known isotonic regression problem we also derive the asymptotic distribution of the likelihood ratio statistic for testing equality of the k populations against the uniform stochastic ordering restriction this asymptotic distribution is of the chi bar square type as discussed by robertson wright and dykstra these distributional results are obtained by appealing to elegant results from empirical process theory and showing that the proposed test is asymptotically distribution free recurrence formulas are derived for the weights of the chi bar square distribution for particular cases the theory developed in this paper is illustrated by an example involving data for survival times for carcinoma of the oropharynx

a new approach based on the genetic algorithm for finding a good shape parameter in solving partial differential equations by kansa s method many radial basis function rbf methods contain a free shape parameter that plays an important role for the accuracy of the method in most papers the authors end up choosing this shape parameter by trial and error or some other ad hoc means in this paper we propose applying the genetic algorithm to determine a good shape parameter of radial basis functions for the solution of partial differential equations we use meshless collocation method based on the radial basis function kansa s method to solve partial differential equations due to the severely ill conditioned matrix arising from using rbf we also consider the truncated singular value decomposition method tsvd for solving system of linear equations which is obtained from kansa s method numerical results show that the proposed algorithm based on the genetic optimization is effective and provides a reasonable shape parameter along with acceptable accuracy of the solution