• Journal of the Korean Statistical Society
• /
• v.20 no.1
• /
• pp.67-76
• /
• 1991

The empirical Bayes version involves ″independent″ repetitions(a sequence) of the component decision problem. With the varying sample size possible, these are not identical components. However, we impose the usual assumption that the parameters sequence $\theta$=($\theta$$_1$, $\theta$$_2$, …) consists of independent G-distributed parameters where G is unknown. We assume that G $\in$ g, a known family of distributions. The sample size $N_i$ and the decisin rule $d_i$ for component i of the sequence are determined in an evolutionary way. The sample size $N_1$ and the decision rule $d_1$$\in$ $D_{N1}$ used in the first component are fixed and chosen in advance. The sample size $N_2$and the decision rule $d_2$ are functions of *see full text($\underline{X}^1$equation omitted), the observations in the first component. In general, $N_i$ is an integer-valued function of *see full text(equation omitted) and, given $N_i$, $d_i$ is a $D_{Ni}$/-valued function of *see full text(equation omitted). The action chosen in the i-th component is *(equation omitted) which hides the display of dependence on *(equation omitted). We construct an empirical Bayes decision rule for estimating normal mean and show that it is asymptotically optimal.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2000.11a
• /
• pp.355-358
• /
• 2000

Magnetoresistance changes of NiFe thin films were investigated as a function of deposition temperature. DC magnetron sputtering was employed to fabricate Ta/NiFe(t)/Ta thin films on Si(001) substrates with in-situ field or with no-field. The thickness(t) of NiFe films was a range of 4 to 15nm. Substrate temperature was a range of 30 to 400$^{\circ}C$. MR measurement was carried out as a function of angle $\theta$, between external field and current direction. MR ratio increased with increasing substrate temperature, also, max. MR ratio was observed in samples deposited at 300$^{\circ}C$. With increasing upto 400$^{\circ}C$, MR ratio was rapidly decreased in the case of thinner NiFe films. In non-field deposited NiFe films, both angle $\theta$=0, 90。, there was no significant change in MR curves. However, MR curves of in-situ field deposited NiFe films were different in both angles $\theta$=0 and 90。

• Journal of the Korean Statistical Society
• /
• v.25 no.1
• /
• pp.95-110
• /
• 1996

We consider the question of efficiency of the Bayes sequential procedure with respect to the optimal fixed sample size Bayes procedure in a simple vs. simple testing problem for data coming from a general nonregular density b(.theta.)h(x)l(x < .theta.). Efficiency is defined in two different ways in these caiculations. Also, the minimax sequential risk (and minimax sequential stratage) is studied as a function of the cost of sampling.

• Journal of Information Science Theory and Practice
• /
• v.1 no.3
• /
• pp.6-11
• /
• 2013

A new explanation, using exponential functions, is given for the S-shaped functional relation between the mean citation score and the proportion of top 10% (and other percentages) publications for the 500 Leiden Ranking universities. With this new model we again obtain an explanation for the concave or convex relation between the proportion of top $100{\theta}%$ publications, for different fractions of ${\theta}$.

• Journal of the Korea Safety Management & Science
• /
• v.2 no.2
• /
• pp.71-83
• /
• 2000

This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, $S_j$, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, ,$theta_j$, is the random variable of environments and the function of probabilistic stress. Also it is assumed that the general stress distribution is uniform, the life distribution for the given hazard rate, $\theta$, is exponential and inverse power law model holds. In this paper, we obtained maximum likelihood estimators of model parameters and the mean life in use stress condition.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1831-1844
• /
• 2016

In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter ${\theta}$. This value is adapted with the value of proximity function ${\delta}$ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter ${\theta}$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that ${\theta}$ takes a default fixed value.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.761-766
• /
• 2013

We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function ${\psi}$.

• Journal of the Korean Statistical Society
• /
• v.24 no.2
• /
• pp.337-347
• /
• 1995

In the problem of some sequential estimation, the stopping times may be written in the form $N(c) = inf{n \geq n_0; n \geq c^2 S^2_n/\delta^2 (\bar{X}_n)}$ where ${s^2_n}$ and ${\bar{X}_n}$ are the sequences of sample variance and sample mean of the independently and identically distributed (i.i.d.) random variables with distribution $F_{\theta}(x), \theta \in \Theta$, respectively, and $\delta$ is either constant or any given positive real valued function. We obtain some asymptotic normality and asymptotic expectation of the N(c) in various limiting situations. Specially, uniform asymptotic normality and uniform asymptotic expectation of the N(c) are given.

• Korean Journal of Soil Science and Fertilizer
• /
• v.23 no.1
• /
• pp.8-14
• /
• 1990

Retardation and hydrodynamic dispersion coefficient necessary for model of water and solute movement in a soil were determined for horizontal soil column with different initial soil water conditions. The soil columns were compacted with sandy loam soil. The bulk density was $1,350+50kg/m^3$, and initial water contents were 0.05, 0.08 and 0.14. Advancement of 0.05% $CaSO_4$ solution was used as the standard and advancements of 0.5% KCl, $CaCl_2$ and $KH_2PO_4$ were compared. Retardation of non-reactive $Cl^-$ was related with the initial soil water content, ${\theta}n$, as ${\theta}/({\theta}-{\theta}n)$, and anion exclusion was ignored. Retardations of active $K^+$, $Ca^{{+}{+}}$ and $H_2PO_4{^-}$ were related as 1/(R+1) $^*{\theta}/({\theta}-{\theta}n)$, in which R was retardation coefficient. Measured R was 0.64 for $K^+$, 0.80 for $Ca^{{+}{+}}$ and 2.6 for $H_2PO_4{^-}$, respectively. Calculated R using Langmuir adsorption isotherm showed fair degree of applicability. Soil water diffusivity, $D({\theta}),m^2/sec$, calculated for different initial water content showed unique function as $$log(D({\theta}))=13.448{\theta}-9.288$$ Hydrodynamic dispersion coefficient of $Cl^-$ above soil water content 0.36 was similar to soil water diffusivity and decreased to near self diffusion coefficient at soil water content near 0.2. Those of $K^+$, $Ca^{{+}{+}}$ $H_2PO_4{^-}$ at soil water content of 0.38 were $5.5{\times}10^{-6}$, $2.4{\times}10^{-6}$ and $7.1{\times}10^{-7}m^2/sec$ and decreased rapidly with decreasing soil water content lower than 0.36.

• Journal of Ecology and Environment
• /
• v.33 no.2
• /
• pp.165-173
• /
• 2010

Soil respiration ($R_S$) is a critical component of the annual carbon balance of forests, but few studies thus far have attempted to evaluate empirical regression models in $R_S$. The principal objectives of this study were to evaluate the relationship between $R_S$ rates and soil temperature (ST) and soil water content (SWC) in soil from a cool-temperate deciduous broad-leaved forest, and to evaluate empirical regression models for the prediction of $R_S$ using ST and SWC. We have been measuring $R_S$, using an open-flow gas-exchange system with an infrared gas analyzer during the snowfree season from 1999 to 2001 at the Takayama Forest, Japan. To evaluate the empirical regression models used for the prediction of $R_S$, we compared a simple exponential regression (flux = $ae^{bt}$Eq. [1]) and two polynomial multiple-regression models (flux = $ae^{bt}{\times}({\theta}{\nu}-c){\times}(d-{\theta}{\nu})^f:$ Eq. [2] and flux = $ae^{bt}{\times}(1-(1-({\theta}{\nu}/c))^2)$: Eq. [3]) that included two variables (ST: t and SWC: ${\theta}{\nu}$) and that utilized hourly data for $R_S$. In general, daily mean $R_S$ rates were positively well-correlated with ST, but no significant correlations were observed with any significant frequency between the ST and $R_S$ rates on periods of a day based on the hourly $R_S$ data. Eq. (2) has many more site-specific parameters than Eq. (3) and resulted in some significant underestimation. The empirical regression, Eq. (3) was best explained by temporal variations, as it provided a more unbiased fit to the data compared to Eq. (2). The Eq. (3) (ST $\times$ SWC function) also increased the predictive ability as compared to Eq. (1) (only ST exponential function), increasing the $R^2$ from 0.71 to 0.78.