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In this paper, the concept of stationary
distribution of Markov chains in random environments (MCIRE) is
introduced, and basic properties of MCIRE are discussed. It is shown
that there exists a stationary distribution of MCIRE under some
natural conditions. In particular, the existence of stationary
distribution of Cogburn's chain are discussed. Moreover, we give an
example of MCIRE which stationary distribution exists.
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In this paper, we discuss the L^rconvergence for weighted sums of arrays of pairwise NQD random
variables. The corresponding results in series of previous papers
are enriched and extended.
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In this paper, we study the construction
of confidence intervals for a probability density function under a
negatively associated (NA) sample based on recursive estimators. It
is shown that the blockwise empirical likelihood (EL) ratio
statistic is asymptotically chi^2-type distributed, which is used
to obtain EL-based confidence interval for the probability density
function.
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This paper studies the lower bound of the
Gini index for the mixed distribution of two distributions with
certain weights by grouped data. These results are used to calculate
the Gini index for China with urban-rural dualistic structure. They
could be expanded to mixed distributions with more than two
sub-distributions and could be used to other real situations, such
as union of countries or areas.
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System failure data from engineering
applications under a competing risks framework is widespread. As a
special form of these data, masked data plays an important role in
engineering. First, we illustrate the form of masked data and
distinguish it from the usual competing risk data. Then for series
systems or parallel systems, two approaches (maximum likelihood
method and Bayesian method) are introduced to analyze the masked
data, and a real data set is analyzed by the two methods.
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The risk factors of commercial medical insurance
losses are investigated in this paper. We conduct an empirical
analysis by fitting the Gamma generalized linear model to a
commercial medical insurance's claims data. The result indicates
that among the many candidate risk factors of medical insurance
losses, the days of hospital stay, the hospital levels, the area
where the insurance business is applied and the insurance level are
significant. On the contrary, the gender and age are insignificant.
Finally, some suggestions are presented, which we believe to be
helpful for future medical insurance's operations and management.
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The estimation of loss distribution is
always a big issue for insurance companies. Several parametric or
nonparametric methods are introduced to fit loss distributions. In
this paper, we propose a method by combining both parametric and
nonparametric methods to solve this problem. We first determine the
threshold between large and small losses by observing the graph of
mean excess function, then use the generalized Pareto distribution,
the parametric method, to fit excess data, and use kernel density
estimation, the nonparametric method, to fit the distribution below
threshold. Finally, we use a data set about Chinese annual
earthquake loss to compare this method with other existing methods.
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This paper studies the detection and
estimation of change points in volatility under nonparametric
regression models. Wavelet methods are applied to construct the test
statistics which can be used to detect change points in volatility.
The asymptotic distributions of the test statistics are established.
We also utilize the test statistics to construct the estimators for
the locations and jump sizes of the change points in volatility. The
asymptotic properties of these estimators are derived. Some
simulation studies are conducted to assess the finite sample
performance of the proposed procedures.
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This paper investigates a dependent
heavy-tailed risk model with constant interest rate, where the claim
sizes are a sequence of upper extended negatively dependent random
variables; the claim arrival process is a general nonnegative
integer-valued counting process, which is independent of the claim
sizes; and the premium process is a general nonnegative and
nondecreasing stochastic process. We obtain an asymptotic result on
the finite-time ruin probability of an insurance company in two
cases, where, one is the claim sizes, the claim arrival process and
the premium process are mutually independent; the other is the tail
probability of the total discounted amount of premiums can be highly
dominated by that of the claim size. Besides, we conduct some
numerical simulations to verify the accuracy of the asymptotic
relation in the obtained result.
