20 July 2009, Volume 25 Issue 4

    

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学术论文
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  A Generalization of the Classical Risk Model

  Zhao Yongxia,Yin Chuancun

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 337-344.

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  In this paper, we extend the classical risk process
  to the process, which is a spectrally negative L\'evy process minus
  a subordinator. Then some results of the ruin probability are
  derived in terms of properties of L\'evy process and some techniques
  from martingale theory. Finally, we derive some properties of
  hitting time and a Pollaczek-Khinchin type formula of the survival
  probability for a spectrally negative L\'evy process.
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  A Kind of Problem of Maximizing the Expected Utility\\from the Terminal Wealth: the Case of Inflation

  Wang Guangchen,Wu Zhen

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 345-353.

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  This paper is concerned with a kind of problem
  of maximizing the expected utility from the terminal wealth in the
  case of inflation. For a class of CRRA utility, we obtain by a
  direct method an agent's explicit optimal portfolio strategy and the
  corresponding maximum expected utility. Moreover, we give some
  economical interpretations. This idea comes from the
  completion-of-square technique of linear quadratic optimal control
  problems. In Section 3, based on the history data of the stock price
  and the inflation rate, the values of the parameters in models are
  estimated with SAS software. And then, the explicit optimal
  portfolio strategy and the maximum expected utility are also given.
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  Generalized Multivariate Beta Distribution

  Lu Zhifeng,Wang Juan

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 354-364.

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  This paper extends the (generalized)
  Beta distribution to the (generalized) multivariate Beta
  distribution. We also study the moment generating function of
  multivariate Beta distribution, obtain the marginal distribution,
  conditional distribution and regression function of the generalized
  multivariate Beta distribution.
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  EM Algorithm for Haplotype Inference Incorporating\\Ungenotyped Individuals in Pedigree Studies

  Zhao Hong,Zhu Wensheng,Guo Jianhua

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 365-374.

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  Haplotype inference and reconstruction have become
  an essential step in linkage analysis and association analysis. The
  methods for haplotype inference are all based on the complete
  genotype data sets. However, genotypes of some individuals in each
  pedigree may be partly missing or ungenotyped. In this article, we
  propose a new EM algorithm to perform haplotype inference
  incorporating ungenotyped individuals in pedigree studies. We also
  give the standard errors of estimated parameters and evaluate the
  performance of our method by simulation studies.
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  Stochastic Prey-Predator Model

  Zhang Shulin,Wei Zhenghong

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 375-380.

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  In this paper, a 2-dimension, nonlinear
  birth-death prey-predator model is established. By generating
  function, we derive the partial differential equations that the mean
  process of our model satisfied and prove that the preys and
  predators will extinct with probability 1.
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  On Stochastic Orders for Order Statistics\\from Normal Distributions

  Huang Yongjun,Zhang Xinsheng

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 381-388.

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  In this paper we obtain some new results on stochastic
  orders for order statistics from normal distributions. Let
  $X_1,\cdots,X_n,X^*_1,\cdots,X^*_n$ be independent normal random
  variables with $X_{i}\sim N(\mu_i,\sigma^2)$ and $X^*_{i}\sim
  N(\mu^*_i,\sigma^2)$, $i=1,\cdots,n$. Suppose that there exists a
  strictly monotone function $f$ such that
  $(f(\mu_{1}),\cdots,f(\mu_{n}))\succeq_{\text{m}}(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,
  we prove that: (i) if $f'(x)f''(x)\geq 0$, then
  $X_{(1)}\leq_{\text{st}}X^*_{(1)}$; (ii) if $f'(x)f''(x)\leq 0$,
  then $X_{(n)}\geq_{\text{st}}X^*_{(n)}$. Moreover, let $X_{i}\sim
  N(\mu,\sigma_i^2)$ and $X^*_{i}\sim N(\mu,\sigma_i^{*2})$,
  $i=1,\cdots,n$. We obtain that
  $({1}/{\sigma_{1}},\cdots,{1}/{\sigma_{n}})\succeq_{\text{m}}
  ({1}/{\sigma^{*}_{1}},\cdots,{1}/{\sigma^{*}_{n}})$ implies that
  $X_{(1)}\leq_{\text{st}}X^*_{(1)}$ and
  $X_{(n)}\geq_{\text{st}}X^*_{(n)}$.
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  Comparison Theorem for Algebraic Convergence\\of Diffusion Processes

  Wang Yingzhe

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 389-397.

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  The relations of different operators for
  reversible Markov processes are studied. And some comparison
  theorems for the algebraic $L^2$ convergence are obtained. Some
  operator can be compared with a special and simple case so that the
  algebraic convergence can be got.
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  Maximum Likelihood Estimation of Multivariate t-Model\\with Rao's Simple Structure and Its Exact Distribution

  Zou Qingming,Wang Jinglong,Zhu Zhongyi

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 398-408.

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  In statistical studying, it is always an interesting
  topic to obtain the estimation and its distribution for an unknown
  parameter in model. In this paper, the maximum likelihood estimation
  of multivariate t-model with Rao's simple structure is considered.
  By the technique of conditional distribution, the exact distribution
  of estimators is obtained.
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  On Exact Distribution of a Class of Supremum-type\\Statistics for Goodness of Fit

  Wei Bocheng:Li Guoying:Zhao Zhiyuan

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 409-420.

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  For goodness of fit tests with simple null hypothesis,
  Zhang (2002) constructed a classes of supremum-type tests. Different
  parameter $\lambda$ and different weighted function $q(t)$ result in
  different tests, including the Kolmogorov-Smirov test, Berk and
  Jones (1979) test and so on. So far, only a few tests corresponding
  to particular $\lambda$ and $q(t)$ have been studied in the
  literature. However, for different problems, the ``best'' tests are
  different. It is necessary to discuss the tests for all $\lambda$
  and the general $q(t)$. In this paper, the exact distributions of
  the test statistics for all $\lambda$ and $q(t)\equiv 1$ are
  derived. When sample size $n$ is large, it takes a long time to get
  the exact quantile. So we give some advice on the computation
  methods for different sample size by simulation studies, and a real
  example to simply illustrate the above methods.
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  Wavelet Estimation in Varying-Coefficient Models

  Lu Yiqiang,Li Zhilin

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 421-432.

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  This paper is concerned with the estimation
  of varying-coefficient model that is frequently used in statistical
  modeling. The wavelet procedures are developed to estimate the
  coefficient functions. The advantage of this approach is to avoid
  the restrictive smoothness requirement for nonparametric function of
  the traditional smoothing approaches for varying-coefficient model,
  such as kernel and local polynomial methods. Furthermore, the
  convergence rate of the wavelet estimators is derived and the
  asymptotic normality is established. Finite sample properties are
  studied through Monte Carlo simulations.
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  Bayesian Assessment for Product's Radiation Hardening\\Performance under Lognormal Distribution

  Han Feng:Wang Jianguo:Qiao DengJiang

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 433-440.

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  We summarize three kinds of data often
  occurred in experiments which are done to estimate the product's
  radiation hardening (RH) performance. A method based on Bayesian
  theory is proposed in this paper. This method is applied to evaluate
  the product's RH performance if the product's RH performance abides
  by the lognormal distribution and the samples are Zero-One data. The
  prior distributions of unknown parameters are also discussed, and
  two examples are given to illustrate the proposed method.
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  Statistical Analysis on the Differences of Writing Style\\Between First 80 Chapters and Last 40 Chapters in \\《Dream of Red Mansions》\\(An Application of Equivalent Test on Two Independent\\Binomial Populations)

  Wei Bocheng

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2009, 25(4): 441-448.

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  Based on data analysis, using the theory and method of
  ``equivalent test on two independent binomial populations'', this
  paper provides a strong evidence that there are significant
  differences on the writing of sights between first 80 chapters and
  last 40 chapters in 《Dream of Red Mansions》. The confidence
  probability of this conclusion is greater than 98\%.