• Journal of the Korean Statistical Society
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• v.34 no.3
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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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• v.10 no.3
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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.

• Journal of Applied Reliability
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• v.11 no.4
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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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• v.41 no.8
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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.

• Journal of Integrative Natural Science
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• v.13 no.2
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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.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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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.

• Journal of Environmental Health Sciences
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• v.33 no.4
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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.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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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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• v.18 no.3
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• pp.377-389
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• 2011

A higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The third generation index $C_{pmk}$ is more powerful than two useful indices $C_p$ and $C_{pk}$ that have been widely used in six sigma industries to assess process performance. In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent the variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, we consider more powerful vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$ that consider the univariate process capability index $C_{pmk}$. First, we examine the process capability index $C_{pmk}$ and plug-in estimator $\hat{C}_{pmk}$. In addition, we derive its asymptotic distribution and variance-covariance matrix $V_{pmk}$ for the vector valued process capability index $C_{pmk}$. Under the assumption of bivariate normal distribution, we study asymptotic confidence regions of our vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$.

• The Journal of the Acoustical Society of Korea
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• v.20 no.2
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• pp.3-9
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• 2001

In this paper, a random number generator for simulation of speech-waveform coders was designed. A random number generator having a desired probability density function and a desired power spectral density is discussed and experimental results are presented. The technique is based on Sondhi algorithm which consists of a linear filter and a memoryless nonlinearity. Several methods of obtaining memoryless nonlinearities for some typical continuous distributions are discussed. Sondhi algorithm is analyzed in the time domain using the diagonal expansion of the bivariate Gaussian probability density function. It is shown that the Sondhi algorithm gives satisfactory results when the memoryless nonlinearity is given in an antisymmetric form as in uniform, Cauchy, binary and gamma distribution. It is shown that the Sondhi algorithm does not perform well when the corresponding memoryless nonlinearity cannot be obtained analytically as in Student-t and F distributions, and when the memoryless nonlinearity can not be expressed in an antisymmetric form as in chi-squared and lognormal distributions.