shape constrained partial identification of a population mean under unknown probabilities of sample selection summary estimating a population mean from a sample obtained with unknown selection probabilities is important in the biomedical and social sciences using a ratio estimator aronow lee 2013 proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed values in this paper we show how to use auxiliary shape constraints on the population outcome distribution such as symmetry or log concavity to obtain tighter bounds on the population mean we use this method to estimate the performance of aymara students an ethnic minority in the north of chile in a national educational standardized test we implement this method in the r package scbounds

dynamics of stochastic delay lotka volterra systems with impulsive toxicant input and levy noise in polluted environments in this paper two stochastic delay lotka volterra systems i e competition system and predator prey system with impulsive toxicant input and levy noise in polluted environments are proposed and investigated under some simple assumptions sufficient and necessary criteria for stability in time average and extinction of each population are established the thresholds between stability in time average and extinction of each model are obtained some recent results are improved and extended greatly

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

semiparametric exponential families for heavy tailed data we propose a semiparametric method for fitting the tail of a heavy tailed population given a relatively small sample from that population and a larger sample from a related background population we model the tail of the small sample as an exponential tilt of the better observed large sample tail using a robust sufficient statistic motivated by extreme value theory in particular our method induces an estimator of the small population mean and we give theoretical and empirical evidence that this estimator outperforms methods that do not use the background sample we demonstrate substantial efficiency gains over competing methods in simulation and on data from a large controlled experiment conducted by facebook

on competitive lotka volterra model in random environments focusing on competitive lotka volterra model in random environments this paper uses regime switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment it is demonstrated that the growth rates of the population sizes of the species are bounded above moreover certain long run average limits of the solution are examined from several angles a partial stochastic principle of competitive exclusion is also derived finally simple examples are used to demonstrate our findings

stochastic kolmogorov type system with infinite delay abstract the paper considers a stochastic functional kolmogorov type population system with infinite delay under the general probability measures main aim is to show that the environment noise will not only suppress a potential population explosion but also make the solution be stochastically ultimately bounded and asymptotic stable moreover two stochastic functional lotka volterra equations as examples are provided to illustrate the main results

remarks on stochastic permanence of population models abstract this paper examines the asymptotic behavior of the stochastic lotka volterra model under markovian switching we show that the stochastic lotka volterra model is stochastically permanent moreover we give another type of stochastic permanence and consider the relationship of two types of stochastic permanence under white noise perturbation

stochastic mutualism model under regime switching with levy jumps abstract this paper is concerned with a stochastic mutualism model under regime switching with levy jumps to begin with the existence and uniqueness of the global positive solution is proved with any given positive initial value then the sufficient conditions for stochastic permanence are established the critical value between extinction and persistence in mean is also obtained in addition under some suitable conditions we proved that there is a unique stationary distribution for the system without levy jumps our method relies on the lyapunov function analysis and the fredholm alternative the results demonstrate that regime switching may contribute to the permanence but jump noise may suppress the permanence

on optimal harvesting problems in random environments this paper investigates the optimal harvesting strategy for a single species living in random environments whose population growth is given by a regime switching diffusion harvesting acts as a stochastic control on the size of the population the objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to the time of extinction of the species the income rate is allowed to be state and environment dependent this is a singular stochastic control problem with both the extinction time and the optimal harvesting policy depending on the initial condition one aspect of receiving payments up to the random time of extinction is that small changes in the initial population size may significantly alter the extinction time when using the same harvesting policy consequently one no longer obtains continuity of the value function using standard arguments for either regular or singular control problems having a fixed time horizon this paper introduces a new sufficient condition under which the continuity of the value function for the regime switching model is established further it is shown that the value function is a viscosity solution of a coupled system of quasi variational inequalities the paper also establishes a verification theorem and based on this theorem an varepsilon optimal harvesting strategy is constructed under certain conditions on the model two examples are analyzed in detail

comparing stochastic lotka volterra predator prey models abstract the phenomenology of population extinction is one of the central themes in population biology which it is an inherently stochastic event in the present investigation we study this problem for three different stochastic models built from a single lotka volterra deterministic model more concretely we study their mean extinction time which satisfies the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients hence we can only compute numerical approximations we suggest a finite element method using freefem our analysis and numerical results allow us to conclude that there are important differences between the three models these differences enable us to choose the most natural way to turn a the deterministic model into a stochastic model

some periodic type solutions for stochastic reaction diffusion equation with cubic nonlinearities abstract in this paper we discuss the bounded solutions stationary solutions periodic solutions almost periodic solutions almost automorphic solutions for stochastic reaction diffusion equation with cubic nonlinearities the main difficulty is the cubic nonlinearities we overcome this difficulty by the semigroup approach the energy estimate method and refined inequality technique

dynamics of a stochastic lotka volterra model perturbed by white noise abstract this paper continues the study of mao et al investigating two aspects of the equation d x t diag x 1 t x n t b a x t d t x t d w t t 0 the first of these is to slightly improve results in x mao s sabais e renshaw asymptotic behavior of stochastic lotka volterra model j math anal 287 2003 141 156 concerning with the upper growth rate of the total quantity i 1 n x i t of species by weakening hypotheses posed on the coefficients of the equation the second aspect is to investigate the lower growth rate of the positive solutions by using lyapunov function technique and using a changing time method we prove that the total quantity i 1 n x i t always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower growth rate

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

stochastic lotka volterra models with multiple delays abstract this paper investigates the asymptotic behavior of the stochastic lotka volterra model with multiple delays by using certain matrix techniques some results on nonexplosion boundedness and pathwise estimation of the model are investigated

using specially designed exponential families for density estimation i this paper have y being portions of the real line or of the plane but the methodology applies just as well to higher dimensionalities and to more complicated spaces estimates of g y are traditionally constructed in two quite different ways by maximum likelihood fitting within some parametric family such as the normal or by nonparametric methods such as kernel density estimation these two methods can be combined by putting an exponential family through a nonparametric estimator the resulting hybrid estimators are the specially designed exponential families of the title figure 1 shows a simple example of this methodology the y are pain i scores for n s 67 women each obtained by averaging the results from a questionnaire administered after an operation the scale runs from y s 0 s w x

modelling the effect of telegraph noise in the sirs epidemic model using markovian switching abstract we discuss the effect of introducing telegraph noise which is an example of an environmental noise into the susceptible infectious recovered susceptible sirs model by examining the model using a finite state markov chain mc first we start with a two state mc and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence we then explain how the results can be generalised to a finite state mc the results for the sir susceptible infectious removed model with markovian switching ms are a special case numerical simulations are produced to confirm our theoretical results

stability in distribution of a stochastic predator prey system with s type distributed time delays abstract this paper concerns the dynamics of a stochastic predator prey lotka volterra system with s type distributed time delays sufficient conditions for the stability in distribution of the solutions sds to the system are obtained the results show that the dynamic scenarios of the sds are completely characterized by two parameters 1 2 among which 1 is just related to the environmental noise while 2 is closely related to both time delays and environmental noises if 2 0 then the distributions of prey predator converge weakly to a unique ergodic invariant distribution ueid if 1 0 2 then the predator goes to extinction while the distributions of prey converge weakly to a ueid if 0 1 then both the predator and prey go to extinction

spectral density ratio models for multivariate extremes the modeling of multivariate extremes has received increasing recent attention because of its importance in risk assessment in classical statistics of extremes the joint distribution of two or more extremes has a nonparametric form subject to moment constraints this article develops a semiparametric model for the situation where several multivariate extremal distributions are linked through the action of a covariate on an unspecified baseline distribution through a so called density ratio model theoretical and numerical aspects of empirical likelihood inference for this model are discussed and an application is given to pairs of extreme forest temperatures supplementary materials for this article are available online

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

the effects of time dependent delays on global stability of stochastic lotka volterra competitive model abstract in this paper a stochastic lotka volterra competitive model with time dependent delays is investigated sufficient conditions for global asymptotic stability of the positive equilibrium are established the obtained result demonstrates that time dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system

interval estimation of population means under unknown but bounded probabilities of sample selection applying concepts from partial identification to the domain of finite population sampling we propose a method for interval estimation of a population mean when the probabilities of sample selection lie within a posited interval the interval estimate is derived from sharp bounds on the hajek 1971 estimator of the population mean we demonstrate the method s utility for sensitivity analysis by applying it to a sample of needles collected as part of a syringe tracking and testing programme in new haven connecticut copyright 2013 oxford university press

on hybrid competitive lotka volterra ecosystems abstract this paper is concerned with competitive lotka volterra model in random environments it uses regime switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment we show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1 moreover we demonstrate that the solution is stochastically bounded continuous and has finite moments furthermore we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results

stationary distribution and periodic solutions for stochastic holling leslie predator prey systems abstract the stochastic autonomous and periodic predator prey systems with holling and leslie type functional response are investigated for the autonomous system we prove that there exists a unique stationary distribution which is ergodic by constructing a suitable lyapunov function under relatively small white noise the result shows that stationary distribution doesn t rely on the existence and the stability of the positive equilibrium in the undisturbed system furthermore for the corresponding non autonomous system we show that there exists a positive periodic markov process under relatively weaker condition finally numerical simulations illustrate our theoretical results

asymptotic properties of stochastic hybrid gilpin ayala system with jumps this paper focuses on studying the dynamics of the stochastic gilpin ayala model under regime switching with jumps the aim is to analyze what happens under the perturbations of regime switching and jumps some asymptotic properties are investigated and sufficient conditions for stochastic permanence extinction non persistence in the mean and weak persistence are provided the critical value among the extinction non persistence in the mean and weak persistence is obtained our results demonstrate that the dynamics of the model have close relations with the jumps and the stationary distribution of the markov chain

permanence and asymptotic behaviors of stochastic predator prey system with markovian switching and levy noise abstract this paper concerns the dynamics of a stochastic predator prey system with markovian switching and levy noise first the existence and uniqueness of global positive solution to the system is proved then by combining stochastic analytical techniques with m matrix analysis sufficient conditions of stochastic permanence and extinction are obtained furthermore for the stochastic permanence case by means of four constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated finally our conclusions are illustrated through an example

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

orbits in a stochastic goodwin lotka volterra model abstract this paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the lotka volterra model the goodwin model we provide a characterization of orbits in the deterministic highly non linear model we then study a stochastic version with brownian noise introduced via a heterogeneous productivity factor existence conditions for a solution to the system are provided we prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels using stochastic lyapunov techniques for recurrent domains numerical insights are provided

coexistence and exclusion of stochastic competitive lotka volterra models abstract this work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive lotka volterra model the conditions obtained are close to necessary in addition convergence in distribution of positive solutions of the model is also established a number of numerical examples are given to illustrate our results

stochastic lotka volterra systems with levy noise abstract this paper is concerned with stochastic lotka volterra models perturbed by levy noise firstly stochastic logistic models with levy noise are investigated sufficient and necessary conditions for stochastic permanence and extinction are obtained then three stochastic lotka volterra models of two interacting species perturbed by levy noise i e predator prey system competition system and cooperation system are studied for each system sufficient and necessary conditions for persistence in the mean and extinction of each population are established the results reveal that firstly both persistence and extinction have close relationships with levy noise secondly the interaction rates play very important roles in determining the persistence and extinction of the species

persistence and extinction in stochastic non autonomous logistic systems this paper studies two widely used stochastic non autonomous logistic models for the first system sufficient conditions for extinction non persistence in the mean weak persistence and stochastic permanence are established the critical number between weak persistence and extinction is obtained for the second system sufficient criteria for extinction non persistence in the mean weak persistence in the mean strong persistence in the mean and stochastic permanence are established the critical number between weak persistence in the mean and extinction is obtained it should be pointed out that this research is systematical and complete in fact the behaviors of the two models in every coefficient cases are cleared up by the results obtained in this paper