• Journal of Korea Water Resources Association
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• v.36 no.3 s.134
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• pp.399-411
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• 2003

An approach determining a confidence interval of Nash's observed mean instantaneous unit hydrograph is developed. In the approach, both two parameters are treated as correlated gaussian random variables based on the theory of Box-Cox transformation and the regional similarity relation, so that linear statistical parameter estimation is possible. A parametric bootstrap method is adopted to give the confidence interval of the mean observed hydrograph. The proposed methodology is also applicable to estimate the parameters of Nash's model for un-gauged basins. An application to a watershed has shown that the proposed approach is adequate to assess the uncertainty of the Nash's hydrograph and to evaluate parameters for un-gauged basins.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.851-858
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• 2009

In the last decades, there has been much interest in climate variability because its change has dramatic effects on humanity. Especially, the precipitation data are measured over space and their spatial association is so complicated. So we should take into account such a spatial dependency structure while analyzing the data. However, in linear models for analyzing the data, data sets show severely skewed distribution. In the paper, we consider the Box-Cox transformation to satisfy the normal distribution prior to the analysis, and employ a Bayesian hierarchical framework to investigate the spatial patterns. The data set we considered is monthly average precipitation of the third quarter of 2007 obtained from 347 automated monitoring stations in Contiguous South Korea.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.103-125
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• 2001

The Box-Cox transformation is a well known family of power transformation that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Sample Entropy statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the maximum likelihood procedure, the procedure via artificial regression estimation, and the recently introduced maximization of the Shapiro-Francia W' statistic procedure is given. In addition, we generate a table for the optimal spacings parameter in computing the Sample Entropy statistic.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.29 no.1
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• pp.143-150
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• 2006

Box-Cox model and T-factor method have been widely used to measure economic depreciations for industrial property. The Box-Cox model which combines economic efficiency with depreciation pattern is here extended to the reliability function. To do so a Rayleigh distribution which has been used to estimate the reliability of current assets was chosen as an efficiency curve of marginal productivity. Such an approach provides the possibility to classify the efficiency curves into four categories. It is also possible to analyze the types of depreciation curves. Therefore, the power family of a non-linear Box-Cox model could be set at certain constant values, then the model can be transformed into a linear model to estimate the economic depreciation rates by utilizing the reliability function. Estimating the resultant linear regression equation requires minimal number of observations, while at the same time facilitating the test of hypothesis on depreciation rates.

• Journal of Integrative Natural Science
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• v.13 no.2
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• pp.76-82
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• 2020

If normality of an observed data is not a viable assumption, we can carry out normal-theory analyses by suitable transforming data. Power transformation by Box and Cox, one of the transformation methods, is derived the power which maximized the likelihood function. But it doesn't induces the closed form in mathematical analysis. In this paper, we compose some R the syntax of which is easier than other statistical packages for deriving the power with using numerical methods. Also, by using R, we show the transformed data approximately distributed the normal through Q-Q plot in univariate and bivariate cases with some examples. Finally, we present the value of a goodness-of-fit statistic(AD) and its p-value for normal distribution. In the similar procedure, this method can be extended to more than bivariate case.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.40 no.5
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• pp.465-475
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• 2020

I-D-F curves were induced by Box-Cox transformation using rainfall data from five major cities in Korea: Seoul, Busan, Daegu, Daejeon, and Gwangju, as well as from Sancheong (South Gyeongsang province) and Yeongcheon (North Gyeongsang province) stations. The practicality of the Box-Cox transformation is more scalable than the traditional method of frequency analysis in terms of applicability because it is available even if the analysis data are insufficient to perform general frequency analysis and do not produce an appropriate probability density function. For the case in which rainfall data for the entire period (10-1440 minutes) and short-term period (20, 30, 40, 50 minutes) at the foregoing 7 stations are omitted, there was a relative error of -23.0 % to 14.7 % at a duration of 10 to 60 minutes below the 100-year frequency. Accordingly, rainfall analysis requires inducing I-D-F curves, including for the short term (20, 30, 40, 50 minutes), and if rainfall data are omitted for the short term (20, 30, 40, 50 minutes), it is necessary to increase the existing margin rate depending on the point in order to ensure the safe design of small-scale hydraulic structures.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.29 no.2
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• pp.143-149
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• 1996

Forecasts of the monthly catches of anchovy in Korea were carried out by the seasonal Autoregressive Integrated Moving Average (ARIMA) model and spectral analysis. The seasonal ARIMA model is as follows: $$(1-0.431B)(1-B^{12})Z_t=(1-0.882B^{12})e_t$$ where: $Z_t=value$ at month $t;\;B^{p}$ is a backward shift operator, that is, $B^pZ_t=Z_{t-p};$ and $e_t=error$ term at month t, which is to forecast 24 months ahead the anchovy catches in Korea. The prediction error by the Box-Cox transformation on monthly anchovy catches in Korea was less than that by the logarithmic transformation. The equation of the Box-Cox transformation was $Y'=(Y^{0.58}-1)/0.58$. Forecasts of the monthly anchovy catches for $1991\~1992$, which were compared with the actual catches, had an absolute percentage error (APE) range of $1.0\~63.2\%$. Total observed annual catches in 1991 and 1992 were 170,293 M/T and 168,234 M/T respectively, while the predicted catches were 148,201 M/T and 148,834 M/T $(API\;13.0\%\;and\;11.5\%,\;respectively)$. The spectrum analysis of the monthly catches of anchovy showed some dominant fluctuations in the periods of 2.2, 6.1, 10.2 12.0 and 14.7 months. The spectrum analysis was also useful for selecting the ARIMA model.

• Proceedings of the IEEK Conference
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• 2003.11b
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• pp.255-258
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• 2003

This paper defines Normalized Term Frequency Weighting method for automatic text categorization by using Box-Cox, and then it applies automatic text categorization. Box-Cox transformation is statistical transformation method which makes normalized data. This paper applies that and suggests new term frequency weighting method. Because Normalized Term Frequency is different from every term compared by existing term frequency weighting method, it is general method more than fixed weighting method such as log or root. Normalized term frequency weighting method's reasonability has been proved though experiments, used 8000 newspapers divided in 4 groups, which resulted high categorization correctness in all cases.

• Journal of the Korean Statistical Society
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• v.21 no.1
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• pp.35-46
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• 1992

On Box-Cox transformation, one or few responses are influential on transformation parameter estimator. To detect influential observatins, several diagnostics (Cook and Wang 1983, Hinkley and Wang 1988, Lawrance 1988, Tsai and Wu 1990) have been suggested. We compare these diagnostics and denote the necessity of multiple cases deletion which is important especially when the masking effect is present. Also, analytic expression of Tsai and Wu's diagnostic is given. We suggest a computationally feasible and useful algorithm based on the basic building blocks, and present descriptive examples using artificial data.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.97-106
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• 2000

In time series analysis we generally use Box-Cox power transformation for variance stabilization. In this paper we show that order estimator and one step ahead forecast of transformed AR(1) model are approximately invariant to those of the original model under some assumptions. A small Monte-Carlo simulation is performed to support the results.