Climatic Factors for Limiting Northward Distribution of Eight Temperate Tree Species in Eastern North America

Eight temperate deciduous tree species, Acer rubrum L., A. saccharinum L., A. saccharum Marsh., Belluta alleghaniensis Britton., Fraxinus nigra Marsh., Quercus rubra L., Titia americana L., and Ulmus americana L. in eastern North America, were selected to explore relationship between the northward distribution of temperate tree species and climatic factors. For each species, more than 30 sites at their north limits of distribution were obtained from their distribution maps, and 11 climatic indices at the north limits were computed. The standardized standard deviation (SD) method, which compares the magnitude of variance of climatic indices, was used to detect which climatic parameter was the most important for explaining northward distribution of these species. We presume that the climatic parameter that has the smallest variance at the north limit would be assigned as the dominant climatic factor for limiting the distribution of this species. The results derived from the standardized SD method indicated that the SD value of warmth index (WI) and/or annual biotemperature (ABT) were the smallest among the 11 climatic indices. Since both WI and ABT represent growing season temperature, it suggested that growing season temperature was the most important climatic factor for explaining the northward distribution of these temperate tree species. The relationships between several climatic indices, WI, coldness index (CI), annual precipitation (AP), annual range of temperature (ART) and humid/arid index were also analyzed. As a result, at the north limits of all these species, both WI and CI decreased with an increase of AP, and CI increased with an increase of ART. Besides growing season temperature, precipitation and climatic continentality also have influence on the northward distribution of the temperate trees in eastern North America.

Climatic envelope of evergreen sclerophyllous oaks and their present distribution in the eastern Himalaya and Hengduan Mountains

Evergreen sclerophyllous oaks （the E.S. oaks, Quercus section Heterobalanus） are the dominant species of the local ecosystem in the eastern Himalaya and the Hengduan Mountains, southwest China. In this study, we document the climatic envelope of the seven E.S. oak species and examine the relationships between climate and their distribution. This was done using a principal components analysis （PCA） and multiple regression analysis （MRA） of nine climatic indices. The main climatic envelope of the E.S. oaks were： mean temperature of the warmest month （MTW）= 12.0-19.5℃, warmth index （WI） = 33.2-88.9℃ month, annual biotemperature （BT）=-6.9- -0.3 ℃, coldness index （CI）=-30.4- -10.1 ℃ month, mean temperature of the coldest month （MTC）=-3.7-3.0℃ and annual precipitation （AP）=701-897 mm at the lower limits; and MTW=8.3-16.1℃, WI=15.7-59.1℃ month, BT=3.6-8.9℃, CI=-55.4-19.3℃ month, MTC=8.3-16.1 ℃ and AP=610-811 mm at the upper limits. The climatic range of the E.S. oaks is wide and includes two climatic zones, the cool-temperature zone and the subpolar zone. The PCA and MRA results suggest that the thermal climate plays a major role and precipitation plays a secondary role in controlling the large-scale distribution of the E.S. oaks, except Quercus monimotricha. In thermal regimes, BT and/or MTW are most important for both lower and upper limits of the E.S. oaks. Furthermore, our results indicate that the upper distribution limits of the E.S. oaks are less determined by low temperatures and their duration （CI） than by other factors.

Moments and limiting distribution of a portfolio of whole life annuity policies

A dual random model of a portfolio of variable amount whole life annuity is set with the mth moment of the present value of benefits, and the respective expressions of the moments under the assumption that the force of interest accumulation function is Wiener process or Ornstein-Uhlenbeck process. Furthermore, the limiting distribution of average cost of this portfolio is discussed with the expression of the limiting distribution under the assumption that the force of interest accumulation is an independent increment process.

First exit distribution and path continuity of Hunt processes

This paper gives a characterization of a Hunt process path by the first exit left limit distribution. It is also showed that if the first exit left limit distribution leaving any ball from the center is a uniform distribution on the sphere, then the Levy Processes are a scaled Brownian motion.

Limiting Distribution of Extreme Values for FGM Random Sequences

This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.

CLASSICAL LIMITS FOR THE COEFFICIENT OF VARIATION FOR THE NORMAL DISTRIBUTION

The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6

The CUSUM statistic of change point under NA sequences

In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge,which extends the results obtained under the case of an indepen-dent normal sample and the moving average processes.Finally,the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

Asymptotic inference for AR(1) panel data

A general asymptotic theory is given for the panel data AR(1) model with time series independent in different cross sections. The theory covers the cases of stationary process, local to unity process, unit root process, mildly integrated, mildly explosive and explosive processes. It is assumed that the cross-sectional dimension and time-series dimension are respectively N and T. The results in this paper illustrate that whichever the process is, with an appropriate regularization, the least squares estimator of the autoregressive coefficient converges in distribution to a normal distribution with rate at least O(N-1/3). Since the variance is the key to characterize the normal distribution, it is important to discuss the variance of the least squares estimator. We will show that when the autoregressive coefficient ρ satisfies |ρ| < 1, the variance declines at the rate O((NT)-1), while the rate changes to O(N^(-1) T^(-2)) when ρ = 1 and O(N^(-1)ρ^(-2 T+4)) when |ρ| > 1. ρ = 1 is the critical point where the convergence rate changes radically. The transition process is studied by assuming ρ depending on T and going to 1. An interesting phenomenon discovered in this paper is that, in the explosive case, the least squares estimator of the autoregressive coefficient has a standard normal limiting distribution in the panel data case while it may not has a limiting distribution in the univariate time series case.

DUAL RANDOM MODEL OF INCREASING LIFE INSURANCE FOR MULTIPLE-LIFE STATUS

In this paper the dual random model of increasing life insurance for multiple-life status is discussed.The mth moment of the present value of benefits are calculated and the respective expressions of the moments under joint life status or last- survivor status are presented.Fur-thermore,the limiting distribution of average cost of a portfolio of increasing life insurance for multiple-life status is studied.

A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES

Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.

Almost sure limit theorem for the maximum of a class of quasi-stationary sequences

This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N（Rn＋σXn）（Rn＋σXn）,under the assumption that the entries of Xn are independent but non-identically distributed random variables.It is proved that,almost surely,the empirical spectral distribution of Cn converges weakly to a non-random distribution whose Stieltjes transform satisfies a certain equation.Our result extends the previous one with the entries of Xn are i.i.d.random varibles to a more general case.The proof of the result mainly employs the Stein equation and the cumulant expansion formula of independent random variables.

On Optimal Ordering of Service Parameters of a Coxian Queueing Model with Three Phases

We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are found. The performance measures of this model are obtained and in addition the optimal order of service parameters is given with a theorem by obtaining the loss probabilities of customers in the system. That is, putting the greatest service parameter at first phase and the second greatest service parameter at second phase and the smallest service parameter at third phase makes the loss probability and means waiting time minimum. We also give the loss probability in terms of mean waiting time in the system. is the transition probability from j-th phase?to??phase . In this manner while and this system turns into queueing model and while the system turns into Cox(2) queueing model. In addition, loss probabilities are graphically given in a 3D graph for corresponding system parameters and phase transient probabilities. Finally it is shown with a numeric example that this theorem holds.

Joint Limit Distributions of Exceedances Point Processes and Partial Sums of Gaussian Vector Sequence

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

Identifying the limiting distribution by a general approach of Stein's method

A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.

Asymptotic distributions of non-central studentized statistics

Let X 1, ..., X n be independent and identically distributed random variables and W n = W n (X 1, ..., X n ) be an estimator of parameter ?. Denote T n = (W n ? ? 0)/s n , where s n 2 is a variance estimator of W n . In this paper a general result on the limiting distributions of the non-central studentized statistic T n is given. Especially, when s n 2 is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted χ 2 distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed.

ON ASYMPTOTIC JOINT DISTRIBUTIONS OF EIGENVALUES OF RANDOM MATRICES WHICH ARISE FROM COMPONENTS OF COVARIANCE MODEL

In this paper, the authors derive the asymptotic joint distributions of theeigenvalues of some random matrices which arise from components of covariance model.

Limit Distributions for Generalized Jirina Processes with Immigration

A relationship between continuous state population-size-dependent branching （CSDB） processes with or without immigration and discrete state population-size-dependent branching （DSDB） processes with or without immigration is established via the representation of the former. Based on this relationship, some limiting distributions of CSDB processes with or without immigration are obtained.

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.

THE LIMITING DISTRIBUTIONS OF SOME SUBCLASSES OF THE GENERALIZED NON-CENTRAL t-DISTRIBUTION

A general theorem on the limiting distribution of the generalized t-distribution is obtained,many applications of this theorem to some subclasses of elliptically contoured distributions in cluding multivariate normal and multivariate t distributions are discussed.Further,their limiting distributions by density function are derived.