• Communications for Statistical Applications and Methods
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• v.13 no.2
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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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• v.62 no.3
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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.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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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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• v.11 no.2
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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.

• MALSORI
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• no.66
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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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• v.14 no.3
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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.

• Journal of the Korea Safety Management & Science
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• v.3 no.3
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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.

• Proceedings of the Safety Management and Science Conference
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• 2012.04a
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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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• v.21 no.5
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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.

• Journal of Food Hygiene and Safety
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• v.7 no.2
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• pp.113-121
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• 1992

Food intake data from 228 persons (96 male adult ranging in age from 19 to 54, 27 female adult ranging in age from 20 to 46, 54 boys ranging in age from 9 to 11, and 51 girls ranging in age from 8 to II) were studied with respect to the shape of the underlying probablity distributions. For each menu items distributional shapes of food intake were different. Most of distributions for food intakes from normaJ distributions. From food intake data of 2 meals nutrition intake data are calculated. For each meal, energy, protein, fat, carbohydrate, fiber, calcium, iron, vitamin A, thiamin, ribofavin, niacin and vitamin C were computed and thier distributions were compared with normal distributions. Distributions for adult female showed normal distributions for some food items. For nutrient intake data from male adults, distributions for vitamin C from 1st meal and calcium from 2nd meal were marginal and the remains were differed from normal distributions. For adult female and childern, distiributions for some nutients were differed from normal distributions. It is hard to find special patterns for each nutrient distributions. Therefore the normal distributions assumptions should be verified prior to applying parametric techniques to thier data. If those assumptions are not valid, non-parametric techniques should be used to analyze their data.