• 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.

• 응용통계연구
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• 제22권4호
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• pp.879-891
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• 2009

We developed the projected l-axial skew-normal(LASN) family of distributions for I-axial data. The LASN family of distributions contains the semicircular skew-normal(SCSN) and the circular skew-normal(CSN) families of distributions as special cases. The LASN densities are similar to the wrapped skew-normal densities for the small values of the scale parameter. However CSN densities have more heavy tails than those of the wrapped skew-normal densities on the circle. Furthermore the CSN densities have two modes as the scale parameter increases. The LASN distribution has very convenient mathematical features. We extend the LASN family of distributions to a bivariate case.

• Communications for Statistical Applications and Methods
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• 제11권2호
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• pp.265-274
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• 2004

The paper extends earlier work on the skew-normal distribution, a family of distributions including normal, but with extra parameter to regulate skewness. The present work introduces a singly truncated parametric family that strictly includes a truncated normal distribution, and studies its properties, with special emphasis on the relation with bivariate normal distribution.

• 대한음성학회지:말소리
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• 제66호
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• pp.1-20
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• 2008

The purpose of this study was to investigate the characteristics of fundamental frequency(F0) and amplitude distributions in persons with cerebral palsy(CP) in the reading task. Participants were divided into three groups: 6 persons with spastic CP, 6 persons with athetoid CP and 6 normal persons who are around 15-20 years old. On the results of this study, firstly, in F0 distributions, most of the spastic CPs tended to appear narrow distributions on the basis of mode, but most of the athetoid CPs were opposite, and both of the CP groups tended to distribute highly on lower and higher frequencies than mean and mode. On the other hand, normal persons had a tendency to appear narrow distributions on the basis of mode. Finally, in amplitude distributions, the spastic CPs showed a tendency that there are little differences between the distribution of mode and the others, and most of the athetoid CPs showed a tendency that the distributions of mode were higher than the others. In addition to, the normal persons had a tendency that the distributions of mode were remarkably higher than both of the CP groups.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.697-705
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• 2003

When X and Y have independent normal distributions with equal coefficient of variation, we develop the reference priors for different groups of ordering for the parameters. Propriety of posteriors under reference priors proved. A real example is presented to compare the classical estimator and Bayes estimator.

• 대한안전경영과학회지
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• 제3권3호
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• pp.175-190
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• 2001

We propose, a new process capability index $C_{psk}$(WV) applying the weighted variance control charting method for non-normally distributed. The main idea of the weighted variance method(WVM) is to divide a skewed or asymmetric distribution into two normal distributions from its mean to create two new distributions which have the same mean but different standard deviations. In this paper we propose an example, a distributions generated from the Johnson family of distributions, to demonstrate how the weighted variance-based process capability indices perform in comparison with another two non-normal methods, namely the Clements and the Wright methods. This example shows that the weighted valiance-based indices are more consistent than the other two methods in terms of sensitivity to departure to the process mean/median from the target value for non-normal processes. Second method show using the percentage nonconforming by the Pearson, Johnson and Burr systems. This example shows a little difference between the Pearson system and Burr system, but Johnson system underestimated than the two systems for process capability.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2012년 춘계학술대회
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• pp.573-577
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• 2012

Based on latest research, the parametric quality statistics cannot be used in non-normal process with demand pattern of many-variety and small-volume, since it involves extremely small sample size. The research proposes nonparametric quality statistics according to the number of lot or batch in the non-normal process. Additionally, the nonparametric Process Capability Index (PCI) is used with 14 identified non-normal distributions.

• Communications for Statistical Applications and Methods
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• 제21권5호
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• pp.461-469
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• 2014

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes.

• 한국식품위생안전성학회지
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• 제7권2호
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• pp.113-121
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• 1992

식품섭취조사가 228명을 대상으로 실시되어, 확률분포의 형태에 대한 연구가 시도되었다. (연령이 19세에서 54세인 96명의 성인남자, 연령이 20세에서 46세인 성인여자, 9세에서 11세인 54명의 남나 어린이, 8세에서 11세인 51명의 여자어린이가 조사되었음). 각 메뉴별로 식품 섭취량의 분포는 형태가 달랐으며, 대부분의 식품 섭취량은 정상분포를 하지 않았다. 두 끼니의 영양 섭취량이, 각 끼니별로 에너지, 단백질, 지방, 탄수화물, 섬유소, 칼슘, 철분, 비타민 A, 티아민, 리보플라빈, 라이신, 비타민 C 가 계산되고, 그 분포형태가 정상분포인가 조사되었다. 성인여자의 경우 메뉴에 따라서 정상분포를 보였다. 성인여자의 영양소섭취의 경우, 첫째끼니의 비타민 C 섭취량과 둘째 끼니의 칼슘이 정상분포이고, 다른 것은 정상분포가 아니었다. 성인여자와 어린이의 경우 정상분포를 보인 영양소도 있었다. 각 영양소 섭취량의 분포에서 어떤 특별한 형태를 찾기는 어려웠으며, 식품섭취나 영양섭취가 정상분포를 하고 있다고 가정하기는 어려웠다. 그러므로, 식품 섭취나 영양 섭취 자료에 정상분포의 가정하에 이루어지는 통계분석을 시도하기 위해서는 이 자료가 정상분포가 확인이 필요할 것이다.