15 February 2008, Volume 24 Issue 1

    

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学术论文
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  Mixed Exponential Dispersion Distributions and Their Applications in Insurance Claims

  Mao Zechun, Liu Jine

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 1-11.

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  The mixed exponential dispersion distributions has been studied based on the background in insurance claims. The distribution can be generated by mixing ED$^{*}$ and compound Poisson-Geometric distribution. The steps of fitting the numbers of claims by using moment estimation and the method about hypothesis
  test have been given in the paper. As an example, the data in automobile insurance in China has been investigated.
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  The Seismic Information in the Variety of Groundwater Level

  Li Yong, Zhang Shumei

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 21-27.

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  To dig the seismic information in the groundwater level, a new statistic is proposed basing on the analysis of the relation between the groundwater lever and the seismic catalogue. Furthermore, a method is presented by means of this statistic to find out earthquake precursors. It is shown that this method is valuable.
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  Testing for Change-Point of the First-Order Autoregressive Time Series Models

  Wang Liming

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 28-36.

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  In this paper, we consider the change point problem with the autocorrelated coefficient $\phi$ in the first-order autoregressive time series models when the variance $\sigma^{2}$ is known and unknown. Using maximum likelihood method, we respectively discuss the abrupt change point and the gradual change point problems for the autocorrelated coefficient in first-order autoregressive time
  series models. With several situations, we propose some test statistics detecting the change point of the first-order autoregressive time series models and give the methods for detecting abrupt change point and gradual change point.
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  The Asymptotical Normality of the Renewal Process Generated by Strictly Stationary LPQD Sequences

  Yang Yang, Wang Yuebao

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 37-42.

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  This paper discusses the asymptotical normality of the renewal process generated by strictly stationary LPQD random variables.
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  Some Distributions for Risk Process Perturbed by Diffusion under Interest Force

  Zhao Xia

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 43-51.

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  We consider the risk process perturbed by diffusion under interest force in this article. The integral expressions, continuities, twice continuous differentiability and integro-differential equations about $F_{\delta}(u;x)$, the distribution of the surplus immediately before ruin, and $H_{\delta}(u;x,y)$, the joint distribution of the surplus immediately before ruin and the deficit at ruin are obtained. As
  corollaries, some distributions for the classical risk process that is perturbed by diffusion are also considered. Certainly, it is seen that many results in references may be derived from our conclusions by letting some constant variable zero.
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  Nonnegative Estimation of Variance Components in General Random Effect Model with Balanced Data

  Ye Rendao, Wang Songgui

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 52-62.

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  For general random effect model with balanced data, it is well-known that analysis of variance estimate (ANOVAE) of variance components is the uniformly minimum variance unbiased estimate (UMVUE). This paper establishes a class of invariant quadratic estimators based on ANOVAE of variance components, which contains several important estimators. In the sense of mean square error, it is proved that this class is uniformly superior to ANOVAE under certain conditions. On the basis of this class, we obtain two nonnegative estimators of variance components, which are uniformly superior to ANOVAE and restricted maximum likelihood estimate (REMLE) in the sense of mean square error,respectively. the
  estimators from this class have explicit expressions and are easily computable.
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  Central Limit Theorem for a Class of Super $\alpha$-Symmetric Stable Processes with Immigration

  Wang Xijun

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 63-72.

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  In this paper, we prove two central limit theorems for a class of super $\alpha$-symmetric stable processes with immigration and its occupation time processes, where the immigration is determined by the Lebesgue measure $\lambda$. The distributions of their renormalized processes converge as $t\to+\infty$ to those
  of centered Gaussian variables in $\mathcal{S}'(\mathbb{R}^d)$.
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  The Property for Solutions of the Multi-Dimensional Backward Doubly Stochastic Differential Equations with Jumps

  Sun Xiaojun, Lu Ying

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 73-82.

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  A multi-dimensional backward doubly stochastic differential equations with jumps was studied. The extension of the It\^{o} formula was given under backward doubly stochastic integral. By the extension of the It\^{o} formula, the existence and uniqueness of the solutions were obtained under Lipschitz condition.
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  Asymptotic Distributions of Return for Several Stocks with Trading Volume

  Hu Xijian, Han Dong

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 83-97.

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  In this paper, we present a nonlinear statistical model which describes directly the interaction relationship between stock's return and itself historical volumes
  and prices and other stocks' volumes and prices. Further, we prove that a sequence of the returns can converge in distribution to an exponentially L\'evy stable distribution or L\'evy stable distribution, depending on different value of parameter.
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  Analysis of 2000-2003 New Life Table's Effect on Life Insurance

  Wang Xiuwen, Qian Linyi

  CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(1): 98-106.

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  With the new life table of 2000-2003
  publication, life insurance pays more attention to the mortality
  rate. For example, considering the mortality rate development trends
  and its effect on life insurance in the future. So we should study more about it. To this paper, in the first section, specific background is introduced. As to mortality force, its function are estimated by least square method and credibility test is given in the second section. At the same time, in the third section, it shows the relationship between and, which reflects the mortality force change with time lapse under the life table of 1990-1993、2000-2003. Moreover, generally, the concept of random variable about Brownian motion to the mortality force formula. Also, the parameter estimated and test given as that of section two. Fourthly, it forecast the effect of decreasing mortality trends on net premium of annuity, providing the concrete example to analyze the longevity risk. Lastly, relative remark and recommendation are given.