29 February 2016, Volume 32 Issue 1
    

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  • CHEN MuFa
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 1-22.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    To study some infinite-dimensional subject (the phase transitions
    in statistical physics, for instance), several mathematical tools are developed. One of
    them is the speed estimation of various stabilities/instabilities. This paper collects
    some unexpected, unified, nearly sharp basic estimates of various types of
    stability/instability for the simplest class of Markov processes, the birth-death processes.
    Some motivations and a part of extensions are also discussed. The paper is based on a talk
    presented recently in several international conferences.

  • YE Yinna
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 23-50.
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    The local limit theorems for the minimum of a random walk with
    Markovian increments is given, with using Presman's factorization theory. This result
    implies the asymptotic behaviour of the survival probability for a critical branching
    process in Markovian depended random environment.

  • CHEN Ling, WEI Laisheng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 51-61.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    The Bayes estimators of variance components are derived under
    weighted square loss function for the balanced one-way classification random effects
    model with the assumption that variance component has the conjugate prior distribution.
    The superiorities of the Bayes estimators for variance components to traditional ANOVA
    estimators are studied in terms of the mean square error (MSE) criterion. Finally, a
    remark for main results is given.

  • ZHANG Hongzhi, HAO Ruili, YE Zhongxing, YANG Weiguo
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 62-68.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    In this paper, we mainly studied the limit properties for the
    countable nonhomogeneous Markov chains. We established some limit properties for the
    functions of the countable nonhomogeneous Markov chains with  variables under the
    convergence in the  sense, which extended the similar conclusions for the
    functions with two variables. At last, as a corollary, we given the similar result in
    the homogeneous Markov stock market.

  • KANG Diantong, YAN Lei
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 69-88.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Let  and  be two nonnegative absolutely continuous random
    variables with respective distribution functions  and  such that ,
    right-continuous inverse functions  and , and survival functions
     and , respectively. We write , and say  is
    smaller than  in the DMRL (decreasing mean residual life) order, if the function

    is increasing in .
        Some characterization properties of the DMRL order are investigated. The closure
    and reversed closure properties of the DMRL order are obtained. Meanwhile, some illustrative
    examples that meet the DMRL order are shown as well.
  • OU Hui, HUANG Ya, YANG Xiangqun, ZHOU Jieming
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 89-100.
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    In this paper, we investigate a robust optimal portfolio and
    reinsurance problem under inflation risk for an ambiguity-averse insurer (AAI), who worries
    about uncertainty in model parameters. We assume that the AAI is allowed to purchase
    proportional reinsurance and invest his/her wealth in a financial market which consists of
    a risk-free asset and a risky asset. The objective of the AAI is to maximize the minimal
    expected power utility of terminal wealth. By using techniques of stochastic control theory,
    closed-form expressions for the value function and optimal strategies are obtained.

  • ZHANG Xiaoqin, WANG Min
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2016, 32(1): 101-110.
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    In this paper, considering of the special geometry of compositional
    data, two new methods for estimating missing values in compositional data are introduced. The
    first method uses the mean in the simplex space which mainly finds the -nearest neighbor
    procedure based on the Aitchison distance, combining with two basic operations on the simplex,
    perturbation and powering. As a second proposal the principal component regression imputation
    method is introduced which initially starts from the result of the proposed the mean in the
    simplex. The method uses ilr transformation to transform the compositional data set, and then
    uses principal component regression in a transformed space. The proposed methods are tested
    on real data and simulated data sets, the results show that the proposed methods work well.