• Journal of the Korean Statistical Society
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• 제34권3호
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• pp.245-261
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• 2005

The marginal distribution of X is considered when (X, Y) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini's skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist's approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.895-907
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• 2003

Recent demands for representing the location of multivariate data produce various multivariate medians such as Tukey median, Oja median and spatial median. They are considered as multivariate versions of the median which is widely recognized as a robust alternative to the arithmetic mean. Many studies show that those multivariate median preserve the robustness. However, the effectiveness of those medians is not fully identified. In this note the relative efficiencies of the multivariate medians are investigated in various configurations under the bivariate t-distribution. It is shown that Tukey median outperforms the others in most configurations.

• 한국신뢰성학회지:신뢰성응용연구
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• 제11권4호
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• pp.319-330
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• 2011

We consider the stress-strength model in which a unit of strength $T_2$ is subjected to environmental stress $T_1$. An important measure considered in stress-strength model is the reliability parameter R=P($T_2$ > $T_1$). The greater the value of R is, the more reliable is the unit to perform its specified task. In this article, we consider the situations in which $T_1$ and $T_2$ are both independent and dependent, and have certain bivariate distributions as their joint distributions. To study the effect of dependency on R, we investigate several bivariate distributions of $T_1$ and $T_2$ and compare the values of R for these distributions. Numerical comparisons are presented depending on the parameter values as well.

• Journal of Ecology and Environment
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• 제41권8호
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• pp.223-234
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• 2017

Background: Spatial structure of plants in a population reflects complex interactions of ecological and evolutionary processes. For dioecious plants, differences in reproduction cost between sexes and sizes might affect their spatial distribution. Abiotic heterogeneity may also affect adaptation activities, and result in a unique spatial structure of the population. Thus, we examined sex- and size-related spatial distributions of old-growth forest of dioecious tree Torreya nucifera in extremely heterogeneous Gotjawal terrain of Jeju Island, South Korea. Methods: We generated a database of location, sex, and size (DBH) of T. nucifera trees for each quadrat ($160{\times}300m$) in each of the three sites previously defined (quadrat A, B, C in Site I, II, and III, respectively). T. nucifera trees were categorized into eight groups based on sex (males vs. females), size (small vs. large trees), and sex by size (small vs. large males, and small vs. large females) for spatial point pattern analysis. Univariate and bivariate spatial analyses were conducted. Results: Univariate spatial analysis showed that spatial patterns of T. nucifera trees differed among the three quadrats. In quadrat A, individual trees showed random distribution at all scales regardless of sex and size groups. When assessing univariate patterns for sex by size groups in quadrat B, small males and small females were distributed randomly at all scales whereas large males and large females were clumped. All groups in quadrat C were clustered at short distances but the pattern changed as distance was increased. Bivariate spatial analyses testing the association between sex and size groups showed that spatial segregation occurred only in quadrat C. Males and females were spatially independent at all scales. However, after controlling for size, males and females were spatially separated. Conclusions: Diverse spatial patterns of T. nucifera trees across the three sites within the Torreya Forest imply that adaptive explanations are not sufficient for understanding spatial structure in this old-growth forest. If so, the role of Gotjawal terrain in terms of creating extremely diverse microhabitats and subsequently stochastic processes of survival and mortality of trees, both of which ultimately determine spatial patterns, needs to be further examined.

• 통합자연과학논문집
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• 제13권2호
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• pp.76-82
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• 2020

If normality of an observed data is not a viable assumption, we can carry out normal-theory analyses by suitable transforming data. Power transformation by Box and Cox, one of the transformation methods, is derived the power which maximized the likelihood function. But it doesn't induces the closed form in mathematical analysis. In this paper, we compose some R the syntax of which is easier than other statistical packages for deriving the power with using numerical methods. Also, by using R, we show the transformed data approximately distributed the normal through Q-Q plot in univariate and bivariate cases with some examples. Finally, we present the value of a goodness-of-fit statistic(AD) and its p-value for normal distribution. In the similar procedure, this method can be extended to more than bivariate case.

• 응용통계연구
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• 제22권1호
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• pp.205-220
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• 2009

For modeling skewed semicircular data, we derive new family of the exponential distributions. We extend it to the l-axial exponential distribution by a transformation for modeling any arc of arbitrary length. It is straightforward to generate samples from the f-axial exponential distribution. Asymptotic result reveals two things. The first is that linear exponential distribution can be used to approximate the l-axial exponential distribution. The second is that the l-axial exponential distribution has the asymptotic memoryless property though it doesn't have strict memoryless property. Some trigonometric moments are also derived in closed forms. Maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for goodness of fit test of the l-axial exponential distribution. We finally obtain a bivariate version of two kinds of the l-axial exponential distributions.

• 한국환경보건학회지
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• 제33권4호
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• pp.299-305
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• 2007

Distribution of fecal pollution indicator bacteria and environmental parameter were investigated of urban artificial lakes. An average concentration of temperature, pH, SS, DO, $COD_{Mn}$, T-P, T-N, Turbidity, Chl-a were $21.5^{\circ}C$, 8.07, 116.70 mg/l, 8.66 mg/l, 2.24 mg/1, 0.52 mg/l, 1.71mg/l, 80.54 NTU, and 52.12 mg/l respectively. From the results of bivariate correlation analysis, fecal contamination indicator bacteria were found to be mutually correlated. And turbidity and suspended solid were correlated. From the results of principal component analysis, four factors were extracted. And four factors of variance explained up to 81.5 percentage. Factor 1 was pollution pattern by fecal contamination, factor 2 was physical pollution pattern by pollution source, factor 3 was natural pollution by precipitation, and factor 4 was artificial pollution pattern by organism.

• 응용통계연구
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• 제25권6호
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• pp.999-1008
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• 2012

A Bayesian multiple change-point model for small data is proposed for multivariate means and is an extension of the univariate case of Cheon and Yu (2012). The proposed model requires data from a multivariate noncentral $t$-distribution and conjugate priors for the distributional parameters. We apply the Metropolis-Hastings-within-Gibbs Sampling algorithm to the proposed model to detecte multiple change-points. The performance of our proposed algorithm has been investigated on simulated and real dataset, Hanwoo fat content bivariate data.

• Communications for Statistical Applications and Methods
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• 제18권3호
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• pp.377-389
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• 2011

공정능력지수는 공정능력을 측정하고 분석하기 위하여 매우 중요한 역할을 하는 측도로, 품질수준과 밀접한 관계가 있을 뿐만 아니라 보다 높은 품질수준은 고객들에게 더 큰 만족을 가져다 준다. 제3세대 공정 능력지수 $C_{pmk}$는 gms히 6시그마 산업현장에서 공정능력을 평가하기 위하여 유용하게 사용되는 두 가지 지수 $C_p$와 $C_{pk}$보다 이론적으로 강력한 지수이다. 실제로 제조현장에서 두 가지 이상의 서로 연관이 있는 품질특성치들과 제품에 대한 규격한계들을 사용하여 보다 정확한 공정능력 분석이 필요할 것이다. 이러한 경우에 단순히 하나의 일변량 공정능력지수를 통하여 공정능력분석을 하기 보다는 벡터 공정능력지수나 다변량공정능력지수를 통하여 분석을 수행하는 것이 바람직할 것이다. 본 논문에서는 3세대 공정능력지수 $C_{pmk}$를 고려하여 2차원 벡터 공정능력지수 $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$에 대하여 연구하였다. 우선, $C_{pmk}$에 대한 플러그-인(plug-in) 추정량 $\hat{C}_{pmk}$과 관련하여 핵심내용인 극한 확률분포를 유도하였다. 나아가 이러한 결과를 기초로 이변량 정규분포하에서 공분산 행렬 $V_{pmk}$을 구체적으로 계산하였다. 또한 이 행렬의 추정을 통하여 벡터 공정능력지수 $C_{pmk}$에 대한 근사적인 공동 신뢰영역을 제시함으로써, 본 논문에서의 극한분포 연구결과가 벡터 공정능력지수 $C_{pmk}$에 대한 통계적 추론에 유용하게 활용될 수 있음을 보여주었다.

• 한국음향학회지
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• 제20권2호
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• pp.3-9
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• 2001

본 논문에서는 음성엔코더 (speech-waveform coder) 시뮬레이션에 사용할 수 있는 난수발생기를 설계하였다. 설계된 난수발생기는 규정된 확률밀도함수와 규정된 스펙트럼을 동시에 만족해야 하는 환경에서 필요로 하는 것이다. 선형필터와 메모리가 없는 비선형 회로로 구성되는 Sondhi 알고리즘 [1]을 기반으로 하여 난수발생기를 구현하였고, 균일 분포, 이진 분포, 감마 분포와 같은 연속적인 확률분포함수들을 얻기 위해 필요한 선형필터와 비선형 회로를 구현하는 방법을 연구하였다. 또한 분석적인 방법을 통하여 구현해야 하는 비선형 회로가 비대칭 형태로 표현되지 않는 경우 (카이-제곱 분포, lognormal 분포)와 수학식으로 표현할 수 없는 경우 (Student-t 분포, F 분포)에는 Sondhi 알고리즘이 동작하지 않음을 보였다.