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Department of Statistics and Actuarial Sciences

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Department of Statistics and Actuarial Sciences
Mathematics Building, Block B
Xi'an Jiaotong-Liverpool University
111 Ren'ai Road Suzhou Dushu Lake Science and Education Innovation District , Suzhou Industrial Park
Suzhou,Jiangsu Province,P. R. China,215123
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https://www.xjtlu.edu.cn/en/study/departments/academic-departments/statistics-and-actuarial-science/
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SAS@xjtlu.edu.cn

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1. Approximation of Kolmogorov-Smirnov test statistic

Author:Bai, L;Kalaj, D

Source:STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES,2020,Vol.

Abstract:Motivated by the weak limit of Kolmogorov- Smirnov test statistics, in this contribution, we derive the asymptotics of P{sup(x is an element of[0,1]n) (W(x)vertical bar W(1) = w) > u}, w is an element of R, for large u, where W(x) is the multivariate Brownian sheet based on a distribution function F. The asymptotic results are obtained for general F and some important examples are also shown.
2. Stochastic ordering of minima and maxima from heterogeneous bivariate Birnbaum-Saunders random vectors

Author:Fang, LX;Zhu, XJ;Balakrishnan, N

Source:STATISTICS,2018,Vol.52

Abstract:In this paper, we discuss stochastic comparisons of minima and maxima arising from heterogeneous bivariate Birnbaum-Saunders (BS) random vectors with respect to the usual stochastic order based on vector majorization of parameters. Suppose the bivariate random vectors (X-1, X-2) and (X-1*, X-2*) follow BVBS(alpha(1), beta(1), alpha(2), beta(2),rho) and BVBS(alpha(1)*, beta(1)*, alpha(2)*, beta(2)*,rho) distributions, respectively. Suppose 0 < nu <= 2. We then prove that when alpha(1) = alpha(2) = alpha(1)* = alpha(2)*, (beta(1)*(-1/nu),beta(2)*(-1/nu)) implies X-2: 2* >= st X-1: 2* >= st X-1: 2. These results are subsequently generalized to a wider range of scale parameters. Next, we prove that when beta(1) = beta(2) = beta(1)* = beta(2)*, (1/alpha(1), 1/alpha(2)) >= m (1/alpha(1)*, 1/alpha(2)*) implies X-2: 2 >= st X-2: 2* and X-1: 2 * >= st X-1: 2. Analogous results are then deduced for bivariate log BS distributions as well.
3. On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum-Saunders distribution based on Type-I, Type-II and hybrid censored samples

Author:Zhu, XJ;Bullet, NB;Saulo, H

Source:METRIKA,2019,Vol.82

Abstract:In this paper, we discuss the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of Laplace Birnbaum-Saunders distribution based on Type-I, Type-II and hybrid censored samples. We first derive the relationship between the MLEs of the two parameters and then discuss the monotonicity property of the profile likelihood function. Numerical iterative procedure is then discussed for determining the MLEs of the parameters. Finally, for illustrative purpose, we analyze one real data from the literature and present some graphical illustrations of the approach.
4. A Simple Step-Stress Model for Coherent Systems and Associated Inference Based on System Signatures

Author:Zhu,Xiaojun;Mitra,Debanjan;Balakrishnan,Narayanaswamy

Source:Studies in Systems, Decision and Control,2018,Vol.142

Abstract:Coherent systems are important structures in reliability. In this paper, we discuss the maximum likelihood estimates (MLEs) of model parameters of an system with known signature having an exponential component distribution based on a simple step-stress model. We also develop confidence intervals (CIs) for the model parameters. A detailed Monte Carlo study is carried out to examine the performance of the point and estimates. Finally, a data analysis is performed for illustrating all the inferential methods developed here.
5. Optimal dividend and capital injection strategy with a penalty payment at ruin: Restricted dividend payments

Author:Xu, R;Woo, JK

Source:INSURANCE MATHEMATICS & ECONOMICS,2020,Vol.92

Abstract:In this paper, we study the optimal dividend and capital injection problem with the penalty payment at ruin. The dividend strategy is assumed to be restricted to a small class of absolutely continuous strategies with bounded dividend density. By considering the surplus process killed at the time of ruin, we transform the problem to a combined stochastic and impulse control one up to ruin with a free boundary at zero. We illustrate the theoretical verifications for different types of capital injection strategies comparing to the conventional results given in the literature, where the capital injections are made before the time of ruin. Under the assumption of restricted dividend density, the value function is proved as the unique increasing, bounded, Lipschitz continuous and upper semi-continuous at zero viscosity solution to the corresponding quasi-variational Hamilton-Jacobi-Bellman (HJB) equation. The uniqueness of such class of viscosity solutions is shown by considering its boundary condition at infinity. The optimality of a specific band-type strategy is proved for the case when the premium rate is (i) greater than or (ii) less than the ceiling dividend rate respectively. Some numerical examples are presented under the exponential and gamma claim size assumptions. (c) 2020 Elsevier B.V. All rights reserved.
6. On moment-type estimators for a class of log-symmetric distributions

Author:Balakrishnan, N;Saulo, H;Bourguignon, M;Zhu, XJ

Source:COMPUTATIONAL STATISTICS,2017,Vol.32

Abstract:In this paper, we propose three simple closed form estimators for a class of log-symmetric distributions on . The proposed methods make use of some key properties of this class of distributions. We derive the asymptotic distributions of these estimators. The performance of the proposed estimators are then compared with those of the maximum likelihood estimators through Monte Carlo simulations. Finally, some illustrative examples are presented to illustrate the methods of estimation developed here.
7. Extremes of standard multifractional Brownian motion

Author:Bai, L

Source:STATISTICS & PROBABILITY LETTERS,2020,Vol.159

Abstract:Let SMBH(t), t is an element of (0, infinity) be a standard multifractional Brownian motion(smBm), where H(t) is an element of (0,1) is a function of t. In this paper we derive the exact asymptotics of P{sup(t is an element of[T1, T2)(]) SMBH(t) > u}, u -> infinity for constants T-1, T-2 >= 0 and several forms of H(t). (C) 2020 Elsevier B.V. All rights reserved.
8. Eliminating Re-Burn-In in Semiconductor Manufacturing through Statistical Analysis of Production Test Data

Author:Pham, HV;Demidenko, SN;Merola, GM

Source:2017 IEEE INTERNATIONAL INSTRUMENTATION AND MEASUREMENT TECHNOLOGY CONFERENCE (I2MTC),2017,Vol.

Abstract:Zero Re-Burn-In methodology presented in this paper is based on statistical analysis of the historical manufacturing data on burn-in (BI) and re-burn-in (REBI) tests employed in semiconductor devices manufacturing. The goal is to reduce ( or, if possible, to eliminate) REBI test so to lower the associated manufacturing cost and time while preserving the required low failure rate of the manufactured devices.. The statistical processing and analysis of the production data sets are performed while employing the JMP software. The research has led to development of a logistic regression model capable of predicting results of the REBI tests before actually sending integrated circuit (IC) lots for the re-testing.
9. Play on Demand: Why Do Players Play the Mobile Games They Do

Author:McCauley, B;Merola, G;Gumbley, S

Source:INTERNATIONAL JOURNAL OF E-BUSINESS RESEARCH,2017,Vol.13

Abstract:Due to the penetration of smartphones and associated mobile devices, mobile gaming has become a ubiquitous industry worldwide. Players now have access to games at all times. Extending previous research and the Uses and Gratifications approach this paper presents an alternative conceptual model that can offer explanations towards understanding why players play the mobile game they play most frequently.
10. Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Author:Yang,Yang;Wang,Kaiyong;Liu,Jiajun;Zhang,Zhimin

Source:Journal of Industrial and Management Optimization,2017,Vol.13

Abstract:Consider a bidimensional risk model with two geometric Lévy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Lévy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.
11. Discussion of "Birnbaum-Saunders distribution: A review of models, analysis and applications"

Author:Fang, LX;Zhu, XJ

Source:APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY,2019,Vol.35

12. Exact inference for Laplace distribution under progressive Type-II censoring based on BLUEs

Author:Liu, K;Zhu, XJ;Balakrishnan, N

Source:METRIKA,2018,Vol.81

Abstract:In this paper, upon using the known expressions for the Best Linear Unbiased Estimators (BLUEs) of the location and scale parameters of the Laplace distribution based on a progressively Type-II right censored sample, we derive the exact moment generating function (MGF) of the linear combination of standard Laplace order statistics. By using this MGF, we obtain the exact density function of the linear combination. This density function is then utilized to develop exact marginal confidence intervals (CIs) for the location and scale parameters through some pivotal quantities. Next, we derive the exact density of the BLUEs-based quantile estimator and use it to develop exact CIs for the population quantile. A brief mention is made about the reliability and cumulative hazard functions and as to how exact CIs can be constructed for these functions based on BLUEs. A Monte Carlo simulation study is then carried out to evaluate the performance of the developed inferential results. Finally, an example is presented to illustrate the point and interval estimation methods developed here.
13. Extremes of Gaussian chaos processes with trend

Author:Bai, L

Source:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2019,Vol.473

Abstract:Let X(t) (X-1 (t), ..., X-d(t)), t is an element of [0, S] be a Gaussian vector process and let g(x), x is an element of R-d be a continuous homogeneous function. We are concerned with the exact tail asymptotic of the chaos process g(X(t)), t is an element of [0, S] with a trend function h(t). Both scenarios X(t) is locally-stationary and X(t) is non-stationary are considered. Important examples include the product of Gaussian processes and chi-processes. (C) 2019 Elsevier Inc. All rights reserved.
14. ASYMPTOTICS FOR A BIDIMENSIONAL RISK MODEL WITH TWO GEOMETRIC LEVY PRICE PROCESSES

Author:Yang, Y;Wang, KY;Liu, JJ;Zhang, ZM

Source:JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2019,Vol.15

Abstract:Consider a bidimensional risk model with two geometric Levy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Levy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.
15. Projection sparse principal component analysis: An efficient least squares method

Author:Merola, GM;Chen, GM

Source:JOURNAL OF MULTIVARIATE ANALYSIS,2019,Vol.173

Abstract:We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a given proportion of variance. The computation of these solutions is very efficient. The proposed method compares well with the optimal least squares sparse components. We show that other SPCA methods fail to identify the best sparse approximations of the principal components and explain less variance than our solutions. We illustrate and compare our method with others with extensive simulations and with the analysis of the computational results for nine datasets of increasing dimensions up to 16,000 variables. (C) 2019 Elsevier Inc. All rights reserved.
16. Robust analysis for premium-reserve models in a stochastic nonlinear discrete-time varying framework

Author:Li, R;Pantelous, AA;Yang, L

Source:JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2020,Vol.368

Abstract:The effective management of uncertainty and complexity in premium pricing and reserve accumulation processes provide new challenges to the decision- and policy-makers. In this regard, the implementation of complex mathematical tools and advanced statistical techniques is highly acquired. Over the last three decades, methodologies and applications of robust control theory to finance and economics have received strong attention among researchers and practitioners. However, relatively scant research has been carried out so far in relation to insurance. This paper proposes a stochastic, nonlinear time-varying premium-reserve (P-R) system with Lipschitz-type conditions in discrete-time to explore P-R system's stability, stabilization and H-infinity-control properties. In our case, as an extension of the classical quadratic condition, the one-side Lipschitz conditions are also considered and a nonconvex feasibility problem is formulated and solved. In addition, both robust stochastic stability and a pre-specified disturbance attenuation level can be guaranteed. Finally, numerical examples are presented to illustrate the applicability of theoretical treatment. (C) 2019 Elsevier B.V. All rights reserved.
17. Delay-Dependent Robust Stability Analysis for Premium-Reserve Models in an Arbitrary Regime Switching Discrete-Time Framework

Author:Li, R;Pantelous, AA;Yang, L

Source:ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING,2019,Vol.5

Abstract:In the insurance industry, the actuarial team experiences significant challenges for pricing a competitive but also fair premium and keeping an accurate level of reserve, which leads inevitably to numerous adjustments over time and potentially several millions of US dollars in annual losses. Because the model and parameter uncertainties play key roles for actuaries, decision makers, and policymakers, the implementation of advanced mathematical and statistical techniques is highly required. Over the last two decades, applications of regime switching models to finance and economics have received strong attention among researchers and particularly among market practitioners. This paper attempts to consider how a linear arbitrary regime switching system in discrete-time framework could be applied to calculate the medium- and long- term reserves and the relevant premiums (abbreviated here as the P-R process) from the point of view of an insurer. In this direction, some recently developed techniques from linear robust control theory are applied to explore the stability, stabilization, and robust H infinity-control of a P-R system and the potential effects of abrupt structural changes in the economic fundamentals, as well as the insurer's strategy over a finite time period. Sufficient linear matrix inequality conditions are derived for this treatment. Finally, a numerical example is illustrated.
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