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This paper considers Wilcoxon signed rank
test based on the median ranked set sample. For any fixed set size
in the proposed sampling the asymptotic distribution-free of the
test statistic is established. Then, it is proofed analytically the
Pitman efficacy of the Wilcoxon signed rank test under the median
ranked set sampling is not only higher than that under the simple
random sampling but also superior to the sign test under the median
ranked set sampling.
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Traditional estimations of parameters of
the generalized Pareto distribution (GPD) are generally constrained
by the shape parameter of GPD. Such as: the method-of-moments (MOM),
the probability-weighted moments (PWM), L-moments (LM), the maximum
likelihood estimation (MLE) and so on. In this paper we use the fact
that GPD can be transformed into the exponential distribution and
use the results of parameters estimation for the exponential
distribution, than we propose parameters estimators of the
two-parameter or three-parameter GPD by the least squares method.
Some asymptotic results are provided and the proposed method not
constrained by the shape parameter of GPD. A simulation study is
carried out to evaluate the performance of the proposed method and
to compare them with other methods suggested in this paper. The
simulation results indicate that the proposed method performs better
than others in some common situation.
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In this paper, we study the optimal dividend
problem in a dual risk model, which might be appropriate for
companies that have fixed expenses and occasional profits. Assuming
that dividend payments are subject to both proportional and fixed
transaction costs, our object is to maximize the expected present
value of dividend payments until ruin, which is defined as the first
time the company's surplus becomes negative. This optimization
problem is formulated as a stochastic impulse control problem. By
solving the corresponding quasi-variational inequality (QVI), we
obtain the analytical solutions of the value function and its
corresponding optimal dividend strategy when jump sizes are
exponentially distributed.
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In this paper, some results on the pathwise
exponential stability are established for the weak solutions of
stochastic 2D Navier-Stokes equation driven by noise. Also,
some results and comments concerning the stabilizability and
stabilization of these equations are stated.
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Varying coefficient EV models with
longitudinal data are considered. The local bias-corrected kernel
estimators for the unknown coefficient functions are proposed. It is
shown that the proposed estimators are asymptotically normal under
some suitable conditions, and hence it can be used to construct the
pointwise confidence regions of the coefficient functions. The
finite-sample properties of the proposed procedures are studied
through a simulation study.
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In this paper, we consider the option
pricing problem when the risky underlying assets are driven by
Markov-modulated geometric Brownian motion (GBM). That is, the
market parameters, for instance, the market interest rate, the
appreciation rate and the volatility of the risky asset, depend on
unobservable states of the economy which are modeled by a
continuous-time hidden Markov chain. The market described by the
Markov-modulated GBM model is incomplete in general, and, hence, the
martingale measure is not unique. We adopt the minimal relative
entropy martingale measure (MEMM) for the Markov-modulated GBM model
as the suitable martingale measure and we obtain the MEMM for the
market in general sense.
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We achieves some results of precise asymptotic
in the complete moment convergence of NA random variables.
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This paper proposes a new sampling plan,
the sample space ordering method, to compute the optimum truncated
sequential test in order to overcome the disadvantages of the widely
use sequential sampling methods that IEC1123 has presented. The main
ideal of this new method is to establish an order at the truncated
sequential sample space, and optimize point by point to arrive the
optimal truncated sequential test. The paper presents in detail how
to realize the new plan, and shows that this new plan has most
powerful to control the sample number and least average sample
number comparing with the methods which IEC1123 and SMT have
proposed.
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In this paper, optimal constant-stress
accelerated degradation test plans are developed under the
assumption that the degradation characteristic follows a Gamma
processes. The test stress levels and the proportion of units
allocated to each stress level are determined by D-criterion and
V-criterion. The general equivalence theorem (GET) is used to
verify that the optimized test plans are globally optimum. In
addition, compromise test plans are also studied. Finally, an
example is provided to illustrate the proposed method and a
sensitivity analysis is conducted to investigate the robustness of
optimal plans.
