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2009 Vol.25 Issue.5,Published 2009-09-20

学术论文
449 A Location Invariant Pickands-Type Estimator
Tao Bao
In this paper, the author proposes
a location invariant Pickands-type estimator as the extreme index is
positive. Its weak and strong convergence are proved. Asymptotical
representation and strong convergence rate are derived, and the
optimal choice of $k_2$ is found. At last simulation and comparison
of this new kind of Pickands-type estimator with other known
Pickands-type estimators are considered by using the adaptive
algorithm.
2009 Vol. 25 (5): 449-460 [Abstract] ( 1645 ) [HTML 0KB] [ PDF 312KB] ( 1376 )
461 The CUSUM Control Chart for the Autocorrelated Data\\with Measurement Error
Liu Xiaohong:Wang Zhaojun
As we know, the measurement error often
exists in practice, and affects the performance of quality control
in some cases. The autoregressive process with the measurement error
is investigated in this paper. For detecting the step shift of the
autoregressive process mean with measurement error, a CUSUM control
chart based on the maximum log-likelihood ratio test is obtained.
Simulated in-control and out-of-control ARL's are made for various
measurement error and autocorrelation coefficients. The simulation
results show that this new CUSUM scheme works well when the process
is negatively autocorrelated.
2009 Vol. 25 (5): 461-474 [Abstract] ( 1881 ) [HTML 0KB] [ PDF 220KB] ( 1349 )
475 Assessing Occupational Exposure Via the Unbalanced\\One-Way Random Models
Li Xinmin
A unbalanced one-way random model is considered
for assessing the proportion of workers whose mean exposure exceed
the occupational exposure limit (OEL) based on exposure measurements
to the worker. Hypothesis testing for the relevant parameter of
interest is proposed when the exposure data are unbalanced. The
method is based on the generalize inference. A simulation study is
conducted to compare it with that of Krishnamoorthy and Guo (2005).
Simulation results suggest that the proposed method appears to be
better, especially in very unbalanced design.
2009 Vol. 25 (5): 475-484 [Abstract] ( 1488 ) [HTML 0KB] [ PDF 203KB] ( 1296 )
485 New Multivariate Skew t Distributions Generated\\from Skew Pearson VII Distributions
Wen Yangjun:Zhu Daoyuan
In general, there are a large number of skew
elliptically contoured distributions with hard calculated integral
forms, while skew normal, skew normal scale mixtures, skew Pearson
type VII and skew Pearson type II distributions possess good
structures. Skew t distributions belong to skew Pearson type VII
distributions, therefore, this paper proposes new multivariate skew
t distributions based on multivariate skew Pearson type VII
distributions. Backgrounds and definitions are given, two stochastic
representations and their equivalence are derived.
2009 Vol. 25 (5): 485-498 [Abstract] ( 1769 ) [HTML 0KB] [ PDF 924KB] ( 1435 )
499 The Gerber-Shiu Function for a Sparre Andersen\\Risk Model
Fan Qingzhu:Yin Chuancun
In this paper, we consider a Sparre Andersen risk model in which
the claim inter-arrival distribution is a mixture of an Erlang($n$)
distribution and an Erlang($m$) distribution. Our purpose is to
study the Gerber-Shiu function $\phi_\delta(u)$. First, we show that
$\phi_\delta(u)$ satisfies a higher-order integro-differential
equation, and then we discuss the roots of the generalized
Lundberg's equation. On this basis, we drive the Laplace transform
of $\phi_\delta(u)$ and prove that $\phi_\delta(u)$ satisfies a
renewal equation. Finally, we consider an example.
2009 Vol. 25 (5): 499-512 [Abstract] ( 1946 ) [HTML 0KB] [ PDF 258KB] ( 1274 )
513 Admissibility of Linear Estimators in Multivariate\\Linear Models with Respect to an Incomplete\\Ellipsoidal Restriction
Wu Jianhong
This paper studies the admissibility of
linear estimators in multivariate linear models with respect to an
incomplete ellipsoidal restriction
$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$.
Specifically, we study the influence of the matrix $N$ and
$\Theta_1$ which is the center of a restricted set to the
admissibility of linear estimators in multivariate linear models
with respect to the incomplete ellipsoidal restriction
$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$. The
main results show that the class of admissible linear estimators
with the restriction
$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$ is the
same as the one with the restriction
$\mbox{tr}(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2$ for
$\Theta_1$ and $\Theta_2$ with certain relationship.
2009 Vol. 25 (5): 513-518 [Abstract] ( 1871 ) [HTML 0KB] [ PDF 172KB] ( 1432 )
519 A Note on Weighted Invariance Principle
Li Linyuan:Chen Ping
In this note we generalize Davydov's\ucite{1}
weak invariance principle for stationary processes to a weighted
partial sums of long memory infinite moving average processes. This
note also contains some bounds on the second moments of increments
of some weighted partial sum processes of a general long memory time
series, not necessarily moving average type. These bounds are useful
in proving the tightness in uniform metric of these processes. As a
consequence of continuous mapping theorem, the probability bounds on
certain functions of random variables can be established.
2009 Vol. 25 (5): 519-530 [Abstract] ( 1683 ) [HTML 0KB] [ PDF 212KB] ( 1382 )
531 Inference in Varying-Coefficient Mixed Models\\by Using Smoothing Spline
Lu Yiqiang:Xu Wangli
Varying-coefficients mixed model (VCMM) is
proposed for longitudinal data and the other correlated data. This
model allows flexible functional dependence of the response variable
on the covariates by using varying-coefficients linear part to
present the covariates effects, while accounting the within-subject
correlation by using random effect. In this article, the coefficient
functions are estimated by using smoothing spline and restricted
maximum likelihood is used to estimate the smoothing parameters and
the variance components simultaneously. The performance of the
proposed method is evaluated though some simulation studies, which
show that both the coefficient functions and variance components
could be estimated well for the VCMMs with all kinds of covariance
structures.
2009 Vol. 25 (5): 531-543 [Abstract] ( 1792 ) [HTML 0KB] [ PDF 324KB] ( 1449 )
544 Expected discounted Penalty Function\\for a Thinning Risk Model
Pan Jie:Wang Guojing
In this paper, we consider a risk model in
which the premium arriving number process is a Poisson process with
parameter $\lambda>0$ while the claim number process is the thinning
of the pre- mium arriving number process. Under such a model, we
obtain the integral equation, the integro- differential equation and
the recursive formula for the expected discounted penalty function.
Using the integro-differential equation we get the closed form
expressions for the Laplace transform of the time of ruin and the
deficit at ruin when the premium and the claim sizes are
exponentially distributed.
2009 Vol. 25 (5): 544-552 [Abstract] ( 1721 ) [HTML 0KB] [ PDF 198KB] ( 1437 )
553 The Credibility Model under Balance Loss Function
Wen Limin:Lin Xia:Wang Jinglong
When the insurance company determine the
premium of corresponding risks, the target premium will be usually
considered. In this article, we derived the credibility estimators
under the balanced loss function by means of credibility theory. We
also estimated the unknown parameters and got the empirical Bayes
credibility estimators. Finally, we simulated the results under the
normal case which showed the desired conclusions.
2009 Vol. 25 (5): 553-560 [Abstract] ( 1653 ) [HTML 0KB] [ PDF 219KB] ( 1476 )
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