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2009 Vol.25 Issue.4,Published 2009-07-20

学术论文
337 A Generalization of the Classical Risk Model
Zhao Yongxia,Yin Chuancun
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.
2009 Vol. 25 (4): 337-344 [Abstract] ( 1813 ) [HTML 0KB] [ PDF 216KB] ( 1435 )
345 A Kind of Problem of Maximizing the Expected Utility\\from the Terminal Wealth: the Case of Inflation
Wang Guangchen,Wu Zhen
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.
2009 Vol. 25 (4): 345-353 [Abstract] ( 2035 ) [HTML 0KB] [ PDF 245KB] ( 1487 )
354 Generalized Multivariate Beta Distribution
Lu Zhifeng,Wang Juan
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.
2009 Vol. 25 (4): 354-364 [Abstract] ( 3553 ) [HTML 0KB] [ PDF 237KB] ( 3485 )
365 EM Algorithm for Haplotype Inference Incorporating\\Ungenotyped Individuals in Pedigree Studies
Zhao Hong,Zhu Wensheng,Guo Jianhua
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.
2009 Vol. 25 (4): 365-374 [Abstract] ( 1953 ) [HTML 0KB] [ PDF 268KB] ( 1653 )
375 Stochastic Prey-Predator Model
Zhang Shulin,Wei Zhenghong
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.
2009 Vol. 25 (4): 375-380 [Abstract] ( 1546 ) [HTML 0KB] [ PDF 176KB] ( 1387 )
381 On Stochastic Orders for Order Statistics\\from Normal Distributions
Huang Yongjun,Zhang Xinsheng
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
$X_{(n)}\geq_{\text{st}}X^*_{(n)}$.
2009 Vol. 25 (4): 381-388 [Abstract] ( 1956 ) [HTML 0KB] [ PDF 231KB] ( 1316 )
389 Comparison Theorem for Algebraic Convergence\\of Diffusion Processes
Wang Yingzhe
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.
2009 Vol. 25 (4): 389-397 [Abstract] ( 1522 ) [HTML 0KB] [ PDF 227KB] ( 1218 )
398 Maximum Likelihood Estimation of Multivariate t-Model\\with Rao's Simple Structure and Its Exact Distribution
Zou Qingming,Wang Jinglong,Zhu Zhongyi
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.
2009 Vol. 25 (4): 398-408 [Abstract] ( 1822 ) [HTML 0KB] [ PDF 243KB] ( 1414 )
409 On Exact Distribution of a Class of Supremum-type\\Statistics for Goodness of Fit
Wei Bocheng:Li Guoying:Zhao Zhiyuan
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.
2009 Vol. 25 (4): 409-420 [Abstract] ( 1512 ) [HTML 0KB] [ PDF 252KB] ( 1278 )
421 Wavelet Estimation in Varying-Coefficient Models
Lu Yiqiang,Li Zhilin
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.
2009 Vol. 25 (4): 421-432 [Abstract] ( 1775 ) [HTML 0KB] [ PDF 218KB] ( 1283 )
433 Bayesian Assessment for Product's Radiation Hardening\\Performance under Lognormal Distribution
Han Feng:Wang Jianguo:Qiao DengJiang
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.
2009 Vol. 25 (4): 433-440 [Abstract] ( 1701 ) [HTML 0KB] [ PDF 387KB] ( 1334 )
441 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
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\%.
2009 Vol. 25 (4): 441-448 [Abstract] ( 1573 ) [HTML 0KB] [ PDF 251KB] ( 2227 )
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