• Title/Summary/Keyword: beta distribution function

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Bayesian Algorithms for Evaluation and Prediction of Software Reliability (소프트웨어 신뢰도의 평가와 예측을 위한 베이지안 알고리즘)

  • Park, Man-Gon;Ray
    • The Transactions of the Korea Information Processing Society
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    • v.1 no.1
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    • pp.14-22
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    • 1994
  • This paper proposes two Bayes estimators and their evaluation algorithms of the software reliability at the end testing stage in the Smith's Bayesian software reliability growth model under the data prior distribution BE(a, b), which is more general than uniform distribution, as a class of prior information. We consider both a squared-error loss function and the Harris loss function in the Bayesian estimation procedures. We also compare the MSE performances of the Bayes estimators and their algorithms of software reliability using computer simulations. And we conclude that the Bayes estimator of software reliability under the Harris loss function is more efficient than other estimators in terms of the MSE performances as a is larger and b is smaller, and that the Bayes estimators using the beta prior distribution as a conjugate prior is better than the Bayes estimators under the uniform prior distribution as a noninformative prior when a>b.

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$3{\beta}$[L-Lysinamide-Carbamoyl] Cholesterol Cationic Lipid as a Biocompatible Vector for Efficient Gene Transfer

  • Choi, Joon-Sig;Lee, Eun-Jung;Jang, Hyung-Suk;Park, Jong-Sang
    • BMB Reports
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    • v.33 no.6
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    • pp.476-482
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    • 2000
  • In this paper, we report a new cationic lipid composed of L-lysinamide and cholesterol as a potent gene delivery vector. $3{\beta}$[L-Lysinamide-carbamoyl] cholesterol could self-assemble with plasmid DNA forming discrete lipoplexes. From atomic force microscopic images of the complexes, the size distribution was observed to range from 100 to 150 nm in diameter. The transfection efficiency of this amphiphile on different cell lines was evaluated as a micellar solution in the absence of the fusogenic helper lipid, dioleoyl phosphatidyletbanolamine (DOPE). Transfection experiments were performed as a function of charge ratio (lipid/DNA) and transfection time. Cytotoxicity and in vitro transfection efficiency of the amphiphile was demonstrated and compared with those of commercially available Lipofectin and polyethylenimine (PEI).

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The association between polymorphisms of ${\beta}$-adrenoceptors and preeclampsia

  • Lim, Ji-Hyae;Kim, Shin-Young;Park, So-Yeon;Yang, Jae-Hyug;Han, Jung-Yeol;Hong, Dal-Soo;Choi, June-Seek;Choi, Kyu-Hong;Ryu, Hyun-Mee
    • Journal of Genetic Medicine
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    • v.4 no.2
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    • pp.160-166
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    • 2007
  • Purpose : The ${\beta}$-adrenoceptors are pharmacologically classified into ${\beta}_1$-, ${\beta}_2$- and ${\beta}_3$-adrenoceptor. The gene of each subtype has polymorphisms related to their function (${\beta}_1$-adrenoceptor: Ser49Gly, ${\beta}_2$-adrenoceptor: Gln27Glu, ${\beta}_3$-adrenoceptor: Trp64Arg). The objectives of this study were to analyse the allelic and genotypic distribution of the representative polymorphism of ${\beta}$-adrenoceptors in preeclampsia and to investigate whether combined genotype of ${\beta}$-adrenoceptors may be associated with preeclampsia. Methods : Blood samples were collected from a Korean population (159 preeclamptic pregnancies and 168 normotensive pregnancies). The ${\beta}_1$-, ${\beta}_2$- and ${\beta}_3$-adrenoceptor genotypes was determined using polymerase chain reaction-restriction fragment length polymorphism. Results : There were no differences in allelic and genotypic distribution of ${\beta}_1$- and ${\beta}_2$-adrenoceptor polymorphisms between the two groups. However, the Arg allele of ${\beta}_3$-adrenoceptor polymorphism were more frequent in preecalmpsia than in controls (P<0.05, OR=1.57, 95% CI=1.01-2.46). Moreover, prevalence of genotype carrying heterozygote of ${\beta}_3$-adrenoceptor polymorphism was increased in preeclampsia compared with controls (P<0.05, OR 1.76, 95% CI 1.06-2.92). When combination of the three polymorphisms were evaluated, pregnancies with the particular combined genotype that is consisted of heterozygote of ${\beta}_1$-, ${\beta}_3$-adrenoceptor and wild homozygote of ${\beta}_2$-adrenoceptor (Ser/Gly, Gln/Gln, Trp/Arg), showed a significant increase in the risk of preeclampsia (P<0.05, OR=3.01, 95% CI 1.12-8.08). Conclusion : A particular combined genotype (Ser/Gly, Gln/Gln, Trp/Arg) of - adrenoceptors was associated with the risk of preeclampsia.

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Transforming Growth Factor-β3 Gene SfaN1 Polymorphism in Korean Nonsyndromic Cleft Lip and Palate Patients

  • Kim, Myung-Hee;Kim, Hyo-Jin;Choi, Je-Yong;Nahm, Dong-Seok
    • BMB Reports
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    • v.36 no.6
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    • pp.533-537
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    • 2003
  • The nonsyndromic cleft lip and palate (NSCL/P) is a congenital deformity of multifactorial origin with a relatively high incidence in the oriental population. Various etiologic candidate genes have been reported with conflicting results, according to race and analysis methods. Recently, the ablation of the TGF-${\beta}3$ gene function induced cleft palates in experimental animals. Also, polymorphisms in the TGF-${\beta}3$ gene have been studied in different races; however, they have not been studied in Koreans. A novel A $\rightarrow$ G single nucleotide polymorphism (defined by the endonuclease SfaN1) was identified in intron 5 of TGF-${\beta}3$ (IVS5+104 A > G). It resulted in different genotypes, AA, AG, and GG. The objective of this study was to investigate the relationship between the SfaN1 polymorphism in TGF-${\beta}3$ and the risk of NSCL/P in the Korean population. The population of this study consisted of 28 NSCL/P patients and 41 healthy controls. The distribution of the SfaN1 genotypes was different between the cases and controls. The frequency of the G allele was significantly associated with the increased risk of NSCL/P [odds ratio (OR) = 15.92, 95% confidence interval (CI) = 6.3-41.0]. The risk for the disease increased as the G allele numbers increased (GA genotype: OR = 2.11, 95% CI = 0.38-11.68; GG genotype: OR = 110.2, 95% CI = 10.67 - 2783.29) in NSCL/P. A stratified study in patients revealed that the SfaN1 site IVS5+104A > G substitution was strongly associated with an increased risk of NSCL/P in males (p < 0.001), but not in females. In conclusion, the polymorphism of the SfaN1 site in TGF-${\beta}3$ was significantly different between the NSCL/P patients and the control. This may be a good screening marker for NSCL/P patients among Koreans.

Evaluation of Distribution Coefficient of a Metal Ion in the Presence of n Chelating Agent

  • Baik, Min-Hoon;Lee, Kun-Jai
    • Journal of Energy Engineering
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    • v.1 no.1
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    • pp.97-101
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    • 1992
  • A mathematical model has been developed for an analytical calculation of distribution coefficient (K$_1$) in the presence of a chelating agent, The newley formulated K$\_$D/ is given as a function of the mole fraction of a free metal ion in the solution, ${\beta}$, and will serve as an alternative for the tedious individual measurements of K$\_$D/. This formulation will be used to analyze the effects of the presence of chelating agents on the adsorption capacity of geologic media such as clay minerals and soils. The present method may be a significant progess for the evaluation of the transport phenomena and separation processes of metal ions (or radionuclides) in the presence of chelating agents.

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Transient Responses of an Airplane Taking off from and Landing on a Very Large Floating Structure in Regular Waves (규칙파중 항공기 이.착륙시 초대형 부유식 해양구조물의 천이 응답 해석)

  • 신현경;이호영;임춘규;강점문;윤명철
    • Journal of Ocean Engineering and Technology
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    • v.15 no.1
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    • pp.26-30
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    • 2001
  • Up to now, Most studies of hydroelasticity are about frequency domain analysis. Those aren't suited for analysis of the landing take-off, and dropping of aircraft on a structure. So, the concern of this paper is the transient behavior of a VLFS subjected to dynamic load, induced by airplane landing and take-off. To predict the added mass, damping coefficient, and wave exciting force, the source-dipole distribution method was used in the frequency domain. The responses are accomplished by using the FEM scheme. A time domain analysis method is based on the Newmark β method to pursue the time step procedure, taking advantage of memory effect function for hydrodynamic effects.

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NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATION CORRESPONDING TO CONTINUOUS DISTRIBUTIONS

  • Amini, Mohammad;Soheili, Ali Reza;Allahdadi, Mahdi
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.709-720
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    • 2011
  • We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

Characteristics of Parameters for the Distribution of fatigue Crack Growth Lives wider Constant Stress Intensity factor Control (일정 응력확대계수 제어하의 피로균열전파수명 분포의 파라메터 특성)

  • 김선진
    • Journal of Ocean Engineering and Technology
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    • v.17 no.2
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    • pp.54-59
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    • 2003
  • The characteristics of the parameters for the probability distribution of fatigue crack growth life, using the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length equals the number of cycle curves that are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratios of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth life seems to follow the 3-parameter Wiubull,, showing a slight dependence on specimen thickness and stress intensity level. The shape parameter, $\alpha$, does not show the dependency of thickness and stress intensity level, but the scale parameter, $\beta$, and location parameter, ${\gamma}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

On Some Distributions Generated by Riff-Shuffle Sampling

  • Son M.S.;Hamdy H.I.
    • International Journal of Contents
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    • v.2 no.2
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    • pp.17-24
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    • 2006
  • The work presented in this paper is divided into two parts. The first part presents finite urn problems which generate truncated negative binomial random variables. Some combinatorial identities that arose from the negative binomial sampling and truncated negative binomial sampling are established. These identities are constructed and serve important roles when we deal with these distributions and their characteristics. Other important results including cumulants and moments of the distributions are given in somewhat simple forms. Second, the distributions of the maximum of two chi-square variables and the distributions of the maximum correlated F-variables are then derived within the negative binomial sampling scheme. Although multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information and deeper insight regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of these distributions. We supplement our findings with exact simple computational methods where no interpolations are involved.

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Characteristics of Parameters for the Distribution of Fatigue Crack Growth Lives under Constant Stress Intensity Factor Control (일정 응력확대계수 제어하의 피로균열전파수명 분포의 파라메터 특성에 관하여)

  • Kim, Seon-Jin;Kim, Young-Sik;Jeong, Hyeon-Cheol
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2002.10a
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    • pp.301-306
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    • 2002
  • The characteristics of parameters for the probability distribution of fatigue crack growth lives by the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length - the number of cycles curves are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratio of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth lives seems to follow the 3-parameter Wiubull and shows a slight dependence on specimen thickness and stress intensity level. The shape parameter, ${\alpha}$, does not show the dependency of thickness and stress intensity level, but the scale parameter, ${\beta}$, and location parameter, ${\upsilon}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

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