The k-factor GARMA Process with Infinite Variance Innovations

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. (2008 Diongue, A.K., Guégan, D. (2008). Estimation of k-Factor GIGARCH Process: A Monte Carlo Study. Communications in Statistics-Simulation and Computation 37:2037–2049.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.     

Closure property of consistently varying random variables based on precise large deviation principles

Let X = {X₁, X₂, …} be a sequence of independent but not necessarily identically distributed random variables, and let η be a counting random variable independent of X. Consider randomly stopped sum S_η = ∑^η_{k = 1}X_k and random maximum S_(η) ? max?{S₀, …, S_η}. Assuming that each X_k belongs to the class of consistently varying distributions, on the basis of the well-known precise large deviation principles, we prove that the distributions of S_η and S_(η) belong to the same class under some mild conditions. Our approach is new and the obtained results are further studies of Kizinevi?, Sprindys, and ?iaulys (2016) and Andrulyt?, Manstavi?ius, and ?iaulys (2017).     

A study on cyclic bandwidth sum

Suppose G is a graph of p vertices. A proper labeling f of G is a one-to-one mapping f:V(G)→{1,2,…,p}. The cyclic bandwidth sum of G with respect to f is defined by CBS _f (G)=∑ _uv∈E(G)|f(v)−f(u)| _p , where |x| _p =min {|x|,p−|x|}. The cyclic bandwidth sum of G is defined by CBS(G)=min {CBS _f (G): f is a proper labeling of G}. The bandwidth sum of G with respect to f is defined by BS _f (G)=∑ _uv∈E(G)|f(v)−f(u)|. The bandwidth sum of G is defined by BS(G)=min {BS _f (G): f is a proper labeling of G}. In this paper, we give a necessary and sufficient condition for BS(G)=CBS(G), and use this to show that BS(T)=CBS(T) when T is a tree. We also find cyclic bandwidth sums of complete bipartite graphs. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. Supported in part by the National Science Council under grants NSC91-2115-M-156-001.     

Sum,product and ratio of Pareto and gamma variables

The exact distributions of X+Y, X Y and X/(X+Y) are studied when X and Y are independent Pareto and gamma random variables. Applications are discussed, to real problems in clinical trials, computer networks and economics.     

Simulating random variables using moment-generating functions and the saddlepoint approximation

When we are given only a transform such as the moment-generating function of a distribution, it is rare that we can efficiently simulate random variables. Possible approaches such as the inverse transform using numerical inversion of the transform are computationally very expensive. However, the saddlepoint approximation is known to be exact for the Normal, Gamma, and inverse Gaussian distribution and remarkably accurate for a large number of others. We explore the efficient use of the saddlepoint approximation for simulating distributions and provide three examples of the accuracy of these simulations.     

利用外资的效应分析及外资政策的调整

本文通过对改革开放二十多年来,我国利用外资的绩效分析,及近年来利用外资的新变化,阐明了我国今后利用外资政策的调整及调整的方向。     

一类无平方因子数的k次方和

拓广了无平方因子数ｋ次方和的结果，得到一类无平方因子数ｋ次方和的估计式．     

Asymptotic behaviour of a test statistic for detection of change in mean of vectors

The paper gives an asymptotic distribution of a test statistic for detecting a change in a mean of random vectors with dependent components. The studied test statistic has a form of a maximum of a square Euclidean norms of vectors with components being standardized partial cumulative sums of deviations from means. The limit distribution was obtained using a result of Piterbarg [1994. High deviations for multidimensional stationary Gaussian processes with independent components. In: Zolotarev, V.M. (Ed.), Stability Problems for Stochastic Models, pp. 197–210].     

WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

In this paper, we establish strong laws for weighted sums of negatively associated (NA) random variables which have a higher‐order moment condition. Some results of Bai Z.D. & Cheng P.E. (2000) [Marcinkiewicz strong laws for linear statistics. Statist. and Probab. Lett. 43, 105–112,] and Sung S.K. (2001) [Strong laws for weighted sums of i.i.d. random variables, Statist. and Probab. Lett. 52, 413–419] are sharpened and extended from the independent identically distributed case to the NA setting. Also, one of the results of Li D.L. et al. (1995) [Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8, 49–76,] is complemented and extended.