• Communications for Statistical Applications and Methods
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• 제26권6호
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• pp.583-589
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• 2019

Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

• 한국물환경학회지
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• 제24권6호
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• pp.676-681
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• 2008

The evaluation of the effluent water quality of sewage treatment plant is one of the most important factor in calculating total maximum daily loads (TMDLs). Current method to calculate 95% upper limit of effluent water quality of sewage treatment plant assuming normal distribution of data needs to be implemented in case of non-normal distribution. We have investigated the applicability of percentile ranking method as a non-parametric statistical analysis in case of non-normal distribution of data.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2001년도 정기학술대회
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• pp.311-319
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• 2001

All indices that are now in use assume normally distributed data, and any use of the indices on non-normal data results in inaccurate capability measurements. Therefore, $C_{s}$ is proposed which extends the most useful index to date, the Pearn-Kotz-Johnson $C_{pmk}$, by not only taking into account that the process mean may not lie midway between the specification limits and incorporating a penalty when the mean deviates from its target, but also incorporating a penalty for skewness. Therefore 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 distribution from its mean to create two new distributions which have the same mean but different standard distributions. In this paper we propose an example, a distribution 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 process.s.s.s.

• Journal of the Korean Data and Information Science Society
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• 제18권4호
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• pp.869-878
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• 2007

In this paper a new process capability index $C_{psks}$ is introduced for non-normal process. $C_{psks}$ that is proposed by transformation of the $C_{psks}$ incorporates an additional skewness correction factor in the denominator of $C_{psks}$. The use of each technique is illustrated by reference to a distribution system which includes the Pearson and Johnson functions. Accordingly, $C_{psks}$ is proposed as the process capability measure for non-normal process.

• Journal of the Korean Data and Information Science Society
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• 제18권4호
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• pp.937-943
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• 2007

In this paper a new process incapability index $C^*_{psks}$ is introduced for non-normal process. $C^*_{psks}$ is proposed by transformation of the $C^*_{psks}$. The use of each technique is illustrated by reference to a distribution system which includes the Pearson and Johnson functions. Accordingly, $C^*_{psks}$ is proposed as the process capability measures for non-normal process.

• 대한산업공학회지
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• 제39권2호
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• pp.109-118
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• 2013

We propose a method for estimating coefficients of AR (autoregressive) model which named MLPAR (Maximum Likelihood of Pearson system for Auto-Regressive model). In the present method for estimating coefficients of AR model, there is an assumption that residual or error term of the model follows the normal distribution. In common cases, we can observe that the error of AR model does not follow the normal distribution. So the normal assumption will cause decreasing prediction accuracy of AR model. In the paper, we propose the MLPAR which does not assume the normal distribution of error term. The MLPAR estimates coefficients of auto-regressive model and distribution moments of residual by using pearson distribution system and maximum likelihood estimation. Comparing proposed method to auto-regressive model, results are shown to verify improved performance of the MLPAR in terms of prediction accuracy.

• ETRI Journal
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• 제33권6호
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• pp.949-952
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• 2011

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

• 기술사
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• 제21권4호
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• pp.19-32
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• 1988

Whereas is non-symmetrical distribution manufacturing process the traditional X-chart by Shewhart is not plotted relatively on the central line but plotted on the skew of upper-hand side or lower-hand side. That is to say, for the purpose of producing either upper-specification-oriented items or lower-specification-oriented items, and when we carry out tighter control so as to have them pass only its specifications, the distribution shape naturally has a non-normal distribution. In the Shewhart X-chart, which is the most widely used one in Korea, such skewed distributions make tile plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such short comings is non-normally distributed processes, a distribution-free type of confidence interval can be used, which should be haled on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for non-normal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, and Truncated-normal distributions, may be easily analyzed. To enhance this improvement, I proved the property of practical applications of control chart method by comparing and analyzing the case studies of practical application of special purpose control chart method, and also by introducing the new designed median control chart.

• Wind and Structures
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• 제36권4호
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• pp.249-261
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• 2023

Aerodynamic force coefficients are generally prescribed by an ensemble average of ten and/or twenty 10-minute samples. However, this makes it difficult to identify the exact probability distribution and exceedance probability of the prescribed values. In this study, 12,600 10-minute samples on three tall buildings were measured, and the probability distributions were first identified and the aerodynamic force coefficients corresponding to the specific non-exceedance probabilities (cumulative probabilities) of wind load were then evaluated. It was found that the probability distributions of the mean and fluctuating aerodynamic force coefficients followed a normal distribution. The ratios of aerodynamic force coefficients corresponding to the specific non-exceedance probabilities (C_f,Non) to the ensemble average of 12,600 samples (C_f,Ens), which was defined as an adjusting factor (C_f,Non/C_f,Ens), were less than 2%. The effect of coefficient of variation of wind speed on the adjusting factor is larger than that of the annual non-exceedance probability of wind load. The non-exceedance probabilities of the aerodynamic force coefficient is between P_C,nonex = 50% and 60% regardless of force components and aspect ratios. The adjusting factors from the Gumbel distribution were larger than those from the normal distribution.

• Journal of the Korean Statistical Society
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• 제25권3호
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• pp.393-406
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• 1996

We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.