In this paper, an Erlang(2) risk model with time-dependent
claims is studied under a multi-layer dividend strategy. First, some piecewise
integro-differential equations with certain boundary conditions for the Gerber-Shiu
function are derived. Then, applying these results, some defective renewal equations
and explicit expressions for the Gerber-Shiu function are obtained when the joint
density of the inter-claim time and claim size belongs to the rational family.
In Bayesian analysis, the Markov Chain Monte Carlo (MCMC)
algorithm is an efficient and simple method to compute posteriors. However, the
chain may appear to converge while the posterior is improper, which will leads
to incorrect statistical inferences. In this paper, we focus on the necessary and
sufficient conditions for which improper hierarchical priors can yield proper
posteriors in a multivariate linear model. In addition, we carry out a simulation
study to illustrate the theoretical results, in which the Gibbs sampling and
Metropolis-Hasting sampling are employed to generate the posteriors.
In this paper, we extend the previous Markov-modulated
reflected Brownian motion model discussed in [1] to a Markov-modulated
reflected jump diffusion process, where the jump component is described as a
Markov-modulated compound Poisson process. We compute the joint stationary
distribution of the bivariate Markov jump process. An abstract example with two
states is given to illustrate how the stationary equation described as a system
of ordinary integro-differential equations is solved by choosing appropriate
boundary conditions. As a special case, we also give the sationary distribution
for this Markov jump process but without Markovian regime-switching.
In this paper the local functional limit theorem for increments
of a Brownian motion is derived with large and small deviations, and the local functional
convergence rate for increments of Brownian motion in Holder norm with respect to
(r,p)capacity is estimated.
In this paper, by using central limit theorem of ND sequences
and probability inequality, the precise asymptotics for partial sums of nonstationary
ND sequences is investigated, and the same results with it under that of NA sequences
are obtained.
One key difference of analyzing functional data from
multidimensional data is that one needs to take phase variation (described by
warping functions) into consideration as well as amplitude variation.
Nonparametric estimation of warping functions may not generate summary measures
that are easily interpreted or compared. We propose a local nonlinear parametric
model to capture major local variation including both phase variation and
amplitude variation. The parameters are interpretable, and can be easily
compared among different curves. Simulation and real data analysis are performed
to illustrate the powerfulness of the method.
In this paper, a nonparametric method for reliability
of the stress-strength model is proposed when the dependent stress variable
and strength variable are subject to right censoring. The dependence between
variables is measured by the common Farlie-Gumbel-Morgenstern copula function
and Clayton copula function. Using the empirical process theory, consistency
and asymptotic normality of the proposed estimator is established in this
paper. The results of numerical simulation show that the proposed method
performs well in the case of finite sample. The method proposed in this paper
has a wide application prospect in practice.
Dealing with the missing values is an important object in
the field of data mining. Besides, the properties of compositional data lead to
that traditional imputation methods may get undesirable result if they are directly
used in this type of data. As a result, the management of missing values in
compositional data is of great significant. To solve this problem, this paper
uses the relationship between compositional data and Euclidean data, and proposes
a new method based on Random Forest for missing values in compositional data.
This method has been implemented and evaluated using both simulated and real-world
databases, then the experimental results reveal that the new imputation method
can be widely used in various types of data sets and has good performance than
other methods.