• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.749-764
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• 2003

In this paper we explain that normal theory likelihood-ratio tests(z, t, $x^2$. F) for mean(s) or variance(s) can be geometrically related to volume of difference of two joint pdf's. One is an estimated joint pdf under null parameter space $\omega$ and the other is an estimated joint pdf under full parameter space $\Omega$. For explanations, ‘distance between two distributions’ is defined. We study properties of it, and derive some results on the distance between two multivariate normal distributions.

• Proceedings of the Korean Reliability Society Conference
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• 2001.06a
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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 Korean Society for Quality Management
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• v.34 no.4
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• pp.102-109
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• 2006

This paper investigates the effects of non-normality on the performance of univariate and multivariate cumulative sum(CUSUM) control charts for monitoring the process mean. In-control and out-of-control average run lengths of the charts are examined for the univariate/multivariate lognormal and t distributions. The effects of the reference value and the correlation coefficient under the non-normal distributions are also studied. Simulation results show that the CUSUM charts with small reference values are robust to non-normality but those with moderate or large reference values are sensitive to non-normal data especially to process data from skewed distributions. The performance of the chart to detect mean shift of a process is not invariant to the direction of the shift for skewed distributions.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.421-433
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• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• Journal of the Society of Disaster Information
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• v.5 no.1
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• pp.30-44
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• 2009

Asphalt concrete pavements are often destroyed within the intended design life due to the increasement in traffic volume. The most common types of asphalt concrete pavement damages are permanent deformation and fatigue cracking, and so on. In this research, characteristics of traffic loadings and lateral wheel path distributions are analyzed using the field survey on traffic flow. The obtained traffic characteristics can be used to the decision making for the maintenance policy of roads. According to the traffic lane analysis for the 2nd and 3rd lanes, inner lane vehicles tended to pass to the right side to avoid the opposite side vehicles. In addition, the outside lane vehicles were deviated to the left side to avoid passengers. It is also noted that the lateral wheel path distributions was close to the normal distribution.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.219-229
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• 2010

There have been many researches on the risk management due to rapid increase of various risk factors for financial assets. Aa a method for comprehensive risk management, Value at Risk (VaR) is developed. For estimation of VaR, it is important task to solve the problem of asymmetric distribution of the return rate with heavy tail. Most real distributions of the return rate have high positive kurtosis and low negative skewness. In this paper, some alternative distributions are used to be fitted to real distributions of the return rate of financial asset. And estimates of VaR obtained by using these fitting distributions are compared with those obtained from real distribution. It is found that normal mixture distribution is the most fitted where its skewness and kurtosis of practical distribution are close to real ones, and the VaR estimation using normal mixture distribution is more accurate than any others using other distributions including normal distribution.

• Journal of the Korean Recycled Construction Resources Institute
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• v.6 no.3
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• pp.153-159
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• 2018

Many researches have been carried out on carbonation, a representative deterioration in underground structure. The carbonation of RC (Reinforced Concrete) structure can cause steel corrosion through pH drop in concrete pore water. However extension of service life in RC structures can be obtained through simple surface protection. Unlike the conventional deterministic maintenance technique, probabilistic technique can consider a variation of service life but it deals with only normal distributions. In the work, life time-probability distributions considering not only normal but also log distributions are induced, and repair cost estimation technique is proposed based on the induced model. The proposed technique can evaluate the repair cost through probabilistic manner regardless of normal or log distribution from initial service life and extended service life with repair. When the extended service life through repair has log distribution, repair cost is effectively reduced. The more reasonable maintenance strategy can be set up though actual determination of life-probability distribution based on long term tests and field investigations.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 1996.06c
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• pp.1073-1080
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• 1996

The impact of the input and output probability distributions on the performance of neural networks to forecast two year peak stream flow (cubic meters per second) is examined for two major river basins of the US. The neural network input consisted of drainage area(square kilometers ) and elevation (meters). When data are normally distributed , the neural networks predict much better than when the data are non-normal and have larger tails in their distributions.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.951-958
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• 2010

In this paper, we obtain the restricted maximum likelihood estimators (RMLE's) for means in normal distributions with the ordered mean constraints. The biases and mean squared errors (MSE's) of these RMLE's are approximated by Mote Carlo methods. In every case a substantial savings in MSE is obtained at the expense of a small loss in bias when using RMLE's instead of the unrestricted MLE's.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.87-96
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• 2001

We consider the empirical Bayes estimation problems with the binomial and normal components when the prior distributions are unknown but are assumed to be in certain families. There may be the families of all distributions on the parameter space or subfamilies such as the parametric families of conjugate priors. We treat both cases and establish the asymptotic optimality for the corresponding decision procedures.