• Proceedings of the Korean Statistical Society Conference
• /
• 2005.11a
• /
• pp.159-165
• /
• 2005

Recently, as a result of the growing interest in modelling stationary processes with discrete marginal distributions, several models for integer valued time series have been proposed in the literature. One of theses models is the integer-valued autoregressive(INAR) models. However, when modelling with integer-valued autoregressive processes, there is not yet distributional properties of forecasts, since INAR process contain an accrued level of complexity in using the Steutal and Van Harn(1979) thinning operator 'o'. In this study, a manageable expression for the asymptotic mean square error of predicting more than one-step ahead from an estimated poisson INAR(1) model is derived. And, we present a bootstrap methods developed for the calculation of forecast interval limits of INAR(p) model. Extensive finite sample Monte Carlo experiments are carried out to compare the performance of the several bootstrap procedures.

• Bulletin of the Korean Chemical Society
• /
• v.10 no.3
• /
• pp.273-278
• /
• 1989

The gas-phase reactions of methyl formate with anions, $-NH_2,\;-OH,\;-CH_2CN$, are studied theoretically using the AM1 method. Stationary points are located by the reaction coordinate method, refined by the gradient norm minimization and characterized by the determination of Hessian matrix. Potential energy profiles and the stationary point structures are presented for all conceivable processes. Four reaction paths are found to be possible: formyl proton and methyl proton abstractions, carbonyl addition, and $S_N2$ process. For the most basic anion $-NH_2$ the proton abstraction path is favored, while in other case, $OH\;and\;-CH_2CN$, the carbonyl addition paths are favored. In all cases the $S_N2$ process is the most exothermic, but due to the relatively high activation barrier the process can be ruled out.

• East Asian mathematical journal
• /
• v.13 no.1
• /
• pp.23-32
• /
• 1997

• The Mathematical Education
• /
• v.20 no.3
• /
• pp.27-33
• /
• 1982

• Bulletin of the Korean Mathematical Society
• /
• v.5 no.1
• /
• pp.73-80
• /
• 1968

• Journal of the Korean Statistical Society
• /
• v.25 no.1
• /
• pp.153-159
• /
• 1996

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2006.05a
• /
• pp.1101-1103
• /
• 2006

For a broad class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process) arrivals, we present a distributional Little's law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue for example, we illustrate how to utilize this relation to get the desired distribution of the number of customers.

• Journal of the Korean Statistical Society
• /
• v.25 no.2
• /
• pp.235-241
• /
• 1996

The ordinary least squares estimator of the disturbance variance in the linear regression model with stationary errors is shown to be asymptotically unbiased when the error process has a spectral density bounded from the above and away from zero. Such error processes cover a broad class of stationary processes, including ARMA processes.

• Journal of the Korean Data and Information Science Society
• /
• v.19 no.4
• /
• pp.1345-1352
• /
• 2008

An inventory with constant demand is studied. We adopt a renewal argument to obtain the transient and stationary distribution of the level of the inventory. We show that the stationary distribution can be also derived by making use of either the level crossing technique or the renewal reward theorem. After assigning several managing costs to the inventory, we calculate the long-run average cost per unit time. A numerical example is illustrated to show how we optimize the inventory.

• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.25-35
• /
• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.