• Communications for Statistical Applications and Methods
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• 제22권2호
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• pp.105-120
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• 2015

A large family of distributions arising from distributions of ordered data is proposed which contains other models studied in the literature. This extension subsume many cases of weighted random variables such as order statistics, records, k-records and many others in variety. Such a distribution can be used for modeling data which are not identical in distribution. Some properties of the theoretical model such as moment, mean deviation, entropy criteria, symmetry and unimodality are derived. The proposed model also studies the problem of parameter estimation and derives maximum likelihood estimators in a weighted gamma distribution. Finally, it will be shown that the proposed model is the best among the previously introduced distributions for modeling a real data set.

• 한국대기환경학회지
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• 제22권6호
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• pp.842-850
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• 2006

The role of chlorination reactions in the formation of polychlorinated dibenzofurans (PCDFs) in a municipal waste incinerator was assessed using a chlorination model for predicting PCDF isomer distributions. Complete distributions of PCDF congeners were obtained from a stoker-type municipal waste incinerator operated under 13 test conditions. Samples were collected from the flue gas prior to the gas cleaning system. While total PCDF yields varied by a factor of five to six, the distributions of congeners were similar. A chlorination model, dependent only on the observed distribution of monochlorinated isomers, was developed to predict the distributions of poly-chlorinated isomers formed by chlorination of dibenzofuran (DF). Agreement between predicted and measured PCDF isomer distributions was high for all homologues, supporting the hypothesis that DF chlorination can play an important role in the formation of PCDF byproducts.

• 설비공학논문집
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• 제3권1호
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• pp.1-10
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• 1991

The purpose of this study is to lay groundwork for a complete analysis of two component flow by analyzing a single component flow made of continuous fluid without dispersed phase. In order to achieve uniform velocity distributions which are desirable in designing an optimum spray column direct contact heat exchanger, the influence of injection nozzle orientation has been investigated for axial and radial injections. The results that radial injection ensures more uniform velocity distributions compared to the axial case. The flow characteristics in a spray column have been investigated with various L/D values and inlet velocities, the most uniform internal velocity distributions have been obtained for the case of L/D=10 and 0.1m/sec. In the present investigation, it is shown that radial injection method for the continuous flow is advantageous in obtaining desirable uniform velocity distributions in a spray column. It is also found that as the value of L/D increases and the inlet velocity decreases, the flow improves to be better uniform velocity distributions.

• 충청수학회지
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• 제21권4호
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• pp.501-510
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• 2008

The distribution of the sum of n independent random variables having exponential distributions with different parameters ${\beta}_i$ ($i=1,2,{\ldots},n$) is given in [2], [3], [4] and [6]. In [1], by using Laplace transform, Jasiulewicz and Kordecki generalized the results obtained by Sen and Balakrishnan in [6] and established a formula for the distribution of this sum without conditions on the parameters ${\beta}_i$. The aim of this note is to present a method to find the distribution of the sum of n independent exponentially distributed random variables with different parameters. Our method can also be used to handle the case when all ${\beta}_i$ are the same.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.255-266
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• 2006

This paper proposes a class of distributions which is useful in making inferences about the sum of values from a normal and a doubly truncated normal distribution. It is seen that the class is associated with the conditional distributions of truncated bivariate normal. The salient features of the class are mathematical tractability and strict inclusion of the normal and the skew-normal laws. Further it includes a shape parameter, to some extent, controls the index of skewness so that the class of distributions will prove useful in other contexts. Necessary theories involved in deriving the class of distributions are provided and some properties of the class are also studied.

• Structural Engineering and Mechanics
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• 제62권3호
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• pp.365-372
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• 2017

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

• Earthquakes and Structures
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• 제18권2호
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• pp.233-248
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• 2020

In this article, one of the procedures to design viscous dampers proposed in literature is applied to 3D asymmetric-plan buildings, considering different distributions for the damping coefficients, which are assumed to be proportional to specific structural or response parameters. The main purpose was to investigate the effectiveness of different vertical and in-plan distributions of the damping coefficients of nonlinear viscous dampers for the seismic retrofit of existing buildings. For comparison purposes, all the distributions were applied utilizing both a simplified and an extended method for the 3D structures, where the simplified method takes into account only the translation in the seismic direction, and the extended method considers the translations along the two orthogonal directions together with the floor rotations. The proposed distributions were then applied to a typical case study involving an asymmetric-plan six-storey RC building. The effectiveness of the different distributions was examined through time-history analyses, assuming nonlinear behaviour for both the viscous dampers and the structural elements. The results of the nonlinear dynamic analyses were examined in terms of maximum and residual inter-storey drifts, peak floor accelerations and maximum damper forces.

• 설비공학논문집
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• 제23권6호
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• pp.383-391
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• 2011

Numerical simulations have been conducted for the cylindrical steam reformer having various boundary temperature distributions. $CH_4$, $H_2O$, CO, $H_2$ and $CO_2$ are often generated or destroyed by the reactions, namely the Steam Reofrming(SR) reaction, the Water-Gas Shift (WGS) reaction and the Direct Steam Reforming(DSR) reaction. The SR and the DSR reactions are endothermic reactions, and the WGS reaction is an exothermic reaction. The rate of reactions can be slightly controlled by artificially given boundary temperature distributions. Therefore, the component ratio of the gases at the outlet are different for various boundary temperature distributions, namely the constant, cubic and linear distributions. Among these distributions, the linear temperature distribution is outstanding for efficient hydrogen production of the steam reformer.

• 천문학회보
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• 제39권2호
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• pp.62.1-62.1
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• 2014

Metallicity distribution of globular clusters (GCs) provides an important clue for star formation history of their host galaxy. With an assumption that GCs are generally old, GC colors have been used as a proxy of GC metallicities. Bimodal GC color distributions observed in most large galaxies have, for decades, been interpreted as bimodal metallicity distributions, indicating the presence of two populations within a galaxy. However, the conventional view has been challenged by a new theory that non-linear GC color-metallicity relations (CMRs) can cause a bimodal color distribution even from a single-peaked metallicity distribution. Using the photometric and spectroscopic data of NGC 5128 GCs in combination with stellar population simulation models, we examine the effect of non-linearity in GC CMRs on the transformation of GC color distributions into metallicity distributions. Although, in some colors, offsets are present between observations and models in the CMRs, their overall shape agrees well for various colors. After the offsets are corrected, the observed spectroscopic metallicity distribution is well reproduced via modeled CMRs from various color distributions having different morphologies. On the other hand, the linearly converted metallicity distributions from GC colors show a significant discrepancy with the observed spectroscopic metallicity distribution. We discuss the implications of our results.

• 천문학회보
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• 제37권1호
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• pp.61.1-61.1
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• 2012

We examine both optical and optical/near-infrared (NIR) color distributions of the globular cluster (GC) system in the core of the Coma cluster of galaxies (Abell 1656), centered on the giant elliptical galaxy NGC 4874, to study how non-linearities in the color-metallicity relations of GC systems in large elliptical galaxies are linked to bimodal optical color distributions. Since optical-NIR color distributions of extragalactic GC systems reflect the underlying features of the metallicity distributions, we also present the color-color relation for this GC system. In order to do this, we combine F160W ($H_{160}$) NIR imaging data acquired with the Wide Field Camera 3 IR Channel (WFC3/IR), newly installed on Hubble Space Telescope (HST), with F475W ($g_{475}$) and FF814W ($I_{814}$) optical imaging data from the HST Advanced Camera for Surveys (ACS). To quantitatively explain the feature of color distributions, we use the Gaussian Mixture Modeling (GMM) code. Finally, we show the radial distribution of the GCs in the field of NGC 4874.