• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• International Journal of Highway Engineering
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• v.16 no.5
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• pp.133-142
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• 2014

PURPOSES : The objective was to develop the advanced method which could not explain each observation's specific characteristic in the present negative binomial method that results in under-estimation of the standard error(t-value inflation) and affects the confidence of whole derived results. METHODS : This study dealt with traffic accidents occurring within interchange segment on highway main line with RPNB(Random Parameter Negative Binomial) method that enables to take account of heterogeneity. RESULTS : As a result, AADT and lighting installation type on the road were revealed to have random parameter and in terms of other geometric variables, all were derived as fixed parameter(same effect on every segment). Also, marginal effects were adapted to analyze the relative effects on traffic accidents. CONCLUSIONS : This study proves that RPNB method which considers each observation's specific characteristics is better fitted to the accident data with geometrics. Thus, it is recommended that RPNB model or other methods which could consider the heterogeneity needs to be adapted in accident analysis.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.397-406
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• 2013

We present an improved binomial method for pricing European- and American-type Asian options based on the arithmetic average of the prices of the underlying asset. At each node of the tree we propose a simple algorithm to choose the representative averages among all the effective averages. Then the backward valuation process and the interpolation are performed to compute the price of the option. The simulation results for European and American Asian options show that the proposed method gives much more accurate price than other recent lattice methods with less computational effort.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.397-410
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• 2007

For the two groups data from multivariate binomial distribution, we consider a bootstrap approach to inferring the simultaneous confidence level and its standard error of a collection of the dependent confidence intervals for the difference of proportions with an experimentwise error rate at the a level are presented. The bootstrap method is used to estimate the simultaneous confidence probability for the difference of proportions.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.817-827
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• 2000

In this paper, we investigate the Bayesian approach to random effect binomial regression models with improper prior due to the absence of information on parameter. We also propose a method of estimating the posterior moments and prediction and discuss some general methods for studying model assessment. The methodology is illustrated with Crowder's Seeds Data. Markov Chain Monte Carlo techniques are used to overcome the computational difficulties.

• East Asian mathematical journal
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• v.29 no.5
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• pp.511-519
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• 2013

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.135-145
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• 2012

Traditionally, ERM (Equivalent Random Method) is used to determine number of circuits in an overflow circuit group with rough traffic which has vmr(variance to mean ratio) greater than one. Recently, IPP(Interrupted Poisson Process) approximate method which represents the collective feature of the overflow has been introduced. The negative binomial loss formula can be applied to determine the required number of circuits in the overflow circuit group. In this paper, we deal with the negative binomial loss formula and determination method of number of circuits. We also analyze and compare these three loss formulas.

• Journal of Distribution Science
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• v.12 no.3
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• pp.65-73
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• 2014

Purpose - Aging and fewer economically active people have challenged the assumption of continuous population increases. A new real estate valuation methodology reflecting changes in population structure is thus needed. Research design, data, and methodology - The relationship between demographic change and changes in real estate prices is analyzed using ordinary least squares (OLS) to estimate the parameters, and a population structure change (PSC)-Binomial Option Model is developed to assess the volatility of the estimated parameters. Results based on Seoul and Shanghai data are compared. Results - Results of the DCF method indicate that investing in Seoul is better than investing in Shanghai, but the binomial option indicates the opposite. The PSC-binomial option model, reflecting changes in population structure, yields higher values (24.6 million won in Seoul and 43.3 million won in Shanghai) than those given by the binomial option model. Conclusions - This study indicates that applying changes in population structure to existing research, such as in the binomial option model, represents a more accurate real estate valuation method. Results demonstrate that the new model is more accurate than existing models such as the DCF or binomial option.

• The KIPS Transactions:PartC
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• v.14C no.5
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• pp.439-452
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• 2007

We study on the privacy preserving data mining, PPDM for short, by using randomization. The theoretical PPDM based on the secure multi-party computation techniques is not practical for its computational inefficiency. So we concentrate on a practical PPDM, especially randomization technique. We survey various privacy measures and study on the privacy preserving mining of association rules by using randomization. We propose a new randomization operator, binomial selector, for privacy preserving technique of association rule mining. A binomial selector is a special case of a select-a-size operator by Evfimievski et al.[3]. Moreover we present some simulation results of detecting an appropriate parameter for a binomial selector. The randomization by a so-called cut-and-paste method in [3] is not efficient and has high variances on recovered support values for large item-sets. Our randomization by a binomial selector make up for this defects of cut-and-paste method.