• Journal of Bio-Environment Control
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• v.23 no.1
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• pp.39-42
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• 2014

The objective of this study was to estimate cardinal temperatures for germination of lettuce (Lactuca sativar L.) using bilinear, parabolic, and beta distribution functions. Seeds of lettuce were germinated in a growth chamber at 7 constant temperatures: 10, 14, 16, 20, 24, 28, and $32^{\circ}C$. Four replicates of 100 seeds were placed on two layers of filter paper in a 9 cm petri-dish. Radicle emergence of 1 mm was scored as germination. The time course of germination was modeled using a logistic function. These minimum, optimum, and maximum temperatures were estimated by regression of the inverse of time to 50% germination rate against the temperature gradient. In bilinear function, minimum, optimum, and maximum temperatures were $7.9^{\circ}C$, $23.3^{\circ}C$, and $28.0^{\circ}C$, respectively. In parabolic function, minimum, optimum, and maximum temperatures were $9.7^{\circ}C$, $19.5^{\circ}C$, and $29.4^{\circ}C$, respectively. In beta distribution function, minimum, optimum, and maximum temperatures were $3.7^{\circ}C$, $20.7^{\circ}C$ and $32.0^{\circ}C$, respectively. Minimum, optimum, and maximum ranges of temperatures were $3.7{\sim}9.7^{\circ}C$, $19.5{\sim}23.3^{\circ}C$, and $28.0{\sim}32.0^{\circ}C$, respectively.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.55-63
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• 1995

The characteristics of $I{\lambda}$-optimality are investigated with repsect to other experimental design's criteria, D-and G-optimality. The comparisons are based on D- and G-, and $I{\lambda}$-efficiencies using the Beta(p, q) distribution as a weighting function for $I{\lambda}$-optimality. Results indicate that serious consideration should be given to the $I{\lambda}$-optimality criterion especially when the error variance function is not homogeneous.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.81-95
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• 2008

In this paper, the negative Polya-Eggenberger distribution has been introduced by compounding negative binomial distribution with beta distribution of I-kind which generates a number of univariate contagious or compound (or mixture of) distributions as its particular cases. The distribution is unimode, over dispersed and all of its positive and negative integer moments exist. The difference equation of the proposed model shows that it is a member of the Ord's family of distribution. Some of its interesting properties have been explored besides different methods of estimation been discussed. Finally, the parameters of the proposed model have been estimated by using a computer programme in R-software. Application of the proposed model to some data, available in the literature, has been given and its goodness of fit demonstrated.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.425-435
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• 2016

In this paper, we analyze the inverse statistics of rainfall for 12 regions from 1973 to 2014. We obtain a probability density function f(x) of daily rainfall x, and $f({\tau}_{\rho})$ of the first passage time ${\tau}_{\rho}$ for a given ${\rho}$. Lastly, we derive the relation between ${\rho}$ and ${\tau}_{mean}({\rho})$, i.e., the averaged value of ${\tau}_{\rho}$. The analyses result in the x and ${\tau}_{\rho}$ have stretched exponential distributions. Also, ${\tau}_{mean}({\rho})$ has the form of a stretched exponential function. We derive the shape parameter ${\beta}$ of the distribution, and analyze the characteristics of 12 regional rainfalls.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2000.10a
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• pp.63-67
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• 2000

Up to this day, Most studies of hydroelasticity are inclined to frequency domain atnlysis. Thos amlysis Q the landing, take-4, and dropping of airaqft on a structure. So, the concern of this prrper is a tra a VLFS subjected to dymmic lazd induced by airplane larndirrg and take-off. To predict added mass, dampr exciting force, the source-dipole distribution method were used The responses are accomplished by Fdoimain analysis method is based on Newmark $\beta$ method to pursuit time step pnzcedure taking advantage function for hvdrodvnumic effects.

• Journal of Korean Society for Quality Management
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• v.10 no.2
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• pp.25-33
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• 1982

We discuss a model for acceptance/rejection decision regarding finite populations. The model is based on a beta-binomial prior distribution and additive costs -- relative sampling costs, relative sorting costs and costs of accepted defectives. A substantial part of the paper is devoted to constructing a Bayes sequential sampling acceptance plan (BSSAP) for attributes under the model. It is shown that the Bayes fixed size sampling acceptance plans (BFSAP) are better than the Hald's (1960) single sampling acceptance plans based on a uniform prior. Some tables and examples are provided for comprisons of the minimum Bayes risks of the BSSAP and those of the BFSAP based on a uniform prior and the model.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.539-557
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• 1998

This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.05a
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• pp.1677-1683
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• 2006

Color image segmentation is useful for fast retrieval in large image database. For that purpose, new image segmentation technique based on the probability of pixel distribution in the image is proposed. Color image is first divided into R, G, and B channel images. Then, pixel distribution from each of channel image is extracted to select to which it is similar among the well known probabilistic distribution function-Weibull, Exponential, Beta, Gamma, Normal, and Uniform. We use sum of least square error to measure of the quality how well an image is fitted to distribution. That P.d.f has minimum score in relation to sum of square error is chosen. Next, each image is quantized into 4 gray levels by applying thresholds to the c.d.f of the selected distribution of each channel. Finally, three quantized images are combined into one color image to obtain final segmentation result. To show the validity of the proposed method, experiments on some images are performed.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.64-69
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• 2004

The characteristics of the probability distribution for mechanical properties, e.g. tensile strength, reduction of area, and elongation, for STS304 stainless steel in elevated temperature are investigated. Tensile test is performed by constant crosshead speed controls with 1mm/min. The probability distribution function of measured mechanical properties seems to follow $\alpha$ 3-parameter Weibull, and shows a slight dependence on the temperature. When the temperature is raised, the shape parameter a is increased, but both the scale parameter $\beta$ and location parameter v are decreased.