• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.365-373
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• 2009

Since 1990, identifying the sex of fetus and illegal abortion has brought the sex ratio imbalance at birth in Korea due to a notion of preferring a son to a daughter, socio-economic development, population policy, and so forth. Although there have been many researches such as time series analysis and region difference analysis to monitor this sex ratio imbalance, they have a defect that time and space could not be included in the analysis simultaneously. This study analyzes the sex ratio imbalance at birth, taking into account time and region at the same time. The analysis considered the numbers of male and female babies, who were born as the third or latter in their families, in 2000 and 2001 at 234 Gu / Si / Goon administrative districts. Here, we suggest a mixture model of binomial distributions, assuming heterogeneous populations. The estimation of the location parameters, weights and correlation coefficient of the mixture model is conducted by the EM algorithm, and the heterogeneity of the regions is expressed as a picture using ArcView GIS.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.3
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• pp.371-385
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• 1995

The yield of semiconductor chips is dependent not only on the average defect density but also on the distribution of defects over a wafer. The distribution of defects leads to consider a cluster index. This paper briefly reviews the existing yield prediction models ad proposes a new cluster index, which utilizes the information about the defect location on a wafer in terms of the coefficient of variation. An extensive simulation is performed under a variety of defect distributions and a yield prediction model is derived through the regression analysis to relate the yield with the proposed cluster index and the average number of defects per chip. The performance of the proposed simulation-based yield prediction model is compared with that of the well-known negative binomial model.

• Journal of the Korean Home Economics Association
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• v.35 no.2
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• pp.81-94
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• 1997

The purpose of this study is to identify the possibility of unemployed married women's economic activity by analysing their willingness to work and possible influencial factors on it. This study estimates the effects of independent variables on the dependent available by using Binomial Probit Model. sample are 592 two-parent households. The results of this study are as follows ; The percentage of unemployed married women's willingness to enter into the labor market is 25.2%. Among the variables which have affected their willingness are family variables(family size, the number of children and the existence of children under the age of 6), personal variables(the age, education level and the past working experience) and financial variables(non-wage income, Engel's coefficient, expenditure o leisure activities and the subject judgement of their financial status). It is hard to accept those women's low willingness as is since the most crucial statistically was especially the children of 6 or less among the family variables. That is to say, more favorable conditions of the labor market and inexpensive day-care centres available would certainly encourage married women to be more willing to participate in economic activities as employees.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.28 no.6
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• pp.720-727
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• 1995

A Monte Carlo computer simulation study was conducted to determine the most efficient sampling design for the blue crab dredge capture efficiency experiment performed in Chesapeake Bay, Maryland, U. S. A. The input values were the number of dredge tracks in each experimental area, the number of tows per experiment, the number of experiments, the mean density of crabs per unit area, the negative binomial coefficient, the gear capture efficiency, and the tow error. As a result of the study, a four-track experiment with twenty to twenty-eight tows was estimated to be the best in terms of precision and accuracy of the gear capture efficiency.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.349-358
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• 2017

The cyclic group $C_n={\langle}(12{\cdots}n){\rangle}$ acts on the set $(^{[n]}_k)$ of all k-subsets of [n]. In this action of $C_n$ the number of orbits of size d, for d | n, is $$O^{n,k}_d={\frac{1}{d}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})(^{n/s}_{k/s})$$. Stanton and White [6] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)={\frac{1}{[d]_{q^{n/d}}}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})[^{n/s}_{k/s}]_{q^s}$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a constructive proof for the positivity of coefficients of the orbit polynomial $O^{n,2}_d(q)$.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.551-566
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• 2022

We apply Fourier-Legendre-based integration methods that had been given by Campbell in 2021, to evaluate new rational double hypergeometric sums involving ${\frac{{1}}{\pi}}$. Closed-form evaluations for dilogarithmic expressions are key to our proofs of these results. The single sums obtained from our double series are either inevaluable $_2F_1({\frac{4}{5}})$- or $_2F_1({\frac{1}{2}})$-series, or Ramanujan's ₃F₂(1)-series for the moments of the complete elliptic integral K. Furthermore, we make use of Ramanujan's finite sum identity for the aforementioned ₃F₂(1)-family to construct creative new proofs of Landau's asymptotic formula for the Landau constants.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.9
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• pp.5585-5593
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• 2014

This study tested the hypothesis that the significance of the heterogeneous dispersion parameter in safety performance function (SPF) used to estimate the expected crashes is affected by the endogenous heterogeneous prior distributions, and analyzed the impacts of the mis-specified dispersion parameter on the evaluation results for traffic safety countermeasures. In particular, this study simulated the Poisson means based on the heterogeneous dispersion parameters and estimated the SPFs using both the negative binomial (NB) model and the heterogeneous negative binomial (HNB) model for analyzing the impacts of the model mis-specification on the mean and dispersion functions in SPF. In addition, this study analyzed the characteristics of errors in the crash reduction factors (CRFs) obtained when the two models are used to estimate the posterior means and variances, which are essentially estimated through the estimated hyper-parameters in the heterogeneous prior distributions. The simulation study results showed that a mis-estimation on the heterogeneous dispersion parameters through the NB model does not affect the coefficient of the mean functions, but the variances of the prior distribution are seriously mis-estimated when the NB model is used to develop SPFs without considering the heterogeneity in dispersion. Consequently, when the NB model is used erroneously to estimate the prior distributions with heterogeneous dispersion parameters, the mis-estimated posterior mean can produce large errors in CRFs up to 120%.

• Water for future
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• v.26 no.3
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• pp.113-124
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• 1993

This study aims at the evaluation of the stationary distribution and the emptiness passage time for the effectiveness of water utility in the Keumgang estuary reservoir by two-step transition model. It was taken discrete Markovian correlated inflows for the joint probability of inflows and storage, and was used binomial distribution for inflows distribution. As the results, it was decreased from 0.952 to 0.904 the emptiness probability of the reservoir stationary distribution during 1952-1980, and from 0.900 to 0.829 during 1981-1989, and the average emptiness passage time was increased from 23 days to 37 days during 1952-1980, and from 29 days to 61 days during 1981-1989 at low state of storage. From this, it is found that the emptiness passage time is varied with the increase of the inflows auto-correlation coefficient in the Keumgang estuary reservoir. Therefore, it is understood that auto-correlation coefficient must be taken into consideration for the evaluation of water utility in a small reservoir at drought time.

• Journal of Korean Society of Transportation
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• v.32 no.6
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• pp.662-674
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• 2014

In this study, accident frequency prediction models were constructed by collecting variables such as geometric structures, safety facilities, traffic volume and weather conditions, land use, highway design-satisfaction criteria along 780km (4,372 sections) of 4 lane-highways over 8 areas. As for models, a fixed parameter model and a random parameter model were employed. In the random parameter model, some influences were reversed as the range was expressed based on specific probability in the case of no fixed coefficients. In the fixed parameter model, the influences of independent variables on accident frequency were interpreted by using one coefficient, but in the random parameter model, more various interpretations were took place. In particular, curve radius, securement of shoulder lane, vertical grade design criteria satisfaction showed both positive and negative influence, according to specific probability. This means that there could be a reverse effect depending on the behavioral characteristics of drivers and the characteristics of highway sections. Rather, they influence the increase of accident frequency through the all sections.