• Magazine of the Korean Society of Agricultural Engineers
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• v.29 no.3
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• pp.138-144
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• 1987

This study was conducted to pursue the normalization of frequency distribution by making approach the coefficient of skewness to nearly zero tbrough SMEMAX transformation and to get probable minimum flows can be acquired by means of transforrnation equation which has been derivated by SMEMAX method to the annual minimum flow series of five watersheds along Geum river basin. The results obtained through SMEMAX method were compared with probable minimum flows according to return periods by Type III extremal distribution which has been determined as the best fitted one among probablility distributions for the analysis of minimum flow. All the results obtained through this study are summarized as follows. 1.SMEMAX transformation based on median value was proved to be the best method when the coefficient of skewness has less reliability because of the short duration for the observation and were not affected by accidental outliers. 2.SMEMAX transformation has found to be the best one for the coefficient of skewness to be made nearly zero in comparison with log and cubic root transformation. 3.Probable minimum flows according to the return periods were derivated by transformation equations obtained through theoretical analysis of SMEM AX transformation. 4.In general, probable minimum flows by SMEMAX method were appeared as higher values in the range of five and twenty years and as lower ones in the range of below than five and more than fifty years in return periods respectively, in comparison with the results of type III extremal distribution. 5.Relative errors in the probable minimum flows of SMEMAX method to the results of type III extremal distribution were shown to be within ten percent except those of one hundred years in return periods. 6.SMEMAX method was also confirmed to be useful for the analysis of minimum flow frequency as well as flood frequency analysis.

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.E
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• pp.1-9
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• 1995

It is shown that two step power transformation is more efficient for the normalization of frequency distribution with the coefficient of skewness of zero in comparison with others including SMEMAX and power transformations. It is confirmed that the design low flows calculated using power and two step power transformations used in this study are generally nearer to the observed data as compared with those of SMEMAX transformation at all return periods in the applied watersheds of the Kum, Naktong and Yongsan rivers in Korea.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.4
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• pp.39-47
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• 1992

Derivation of reasonable design low flows was attempted by comparative analysis of design low flows was derived by Power and SMEMAX transformations for the normalizations of skewed distribution and by Type m extremal distribution presented in the first report of this study with annual low flows in the five watersheds of main river basins in Korea. The results were anslyzed and summarized as follows. 1.Basic statistics of annual low flows for the selected watersheds were calculated by using Power and SMEMAX transformations. 2.Power thansformation has found to be the best for the normalization of skewed distribution among others including log, square root and SMEMAX transformations. 3.Design low flows for the selected watersheds were derived by the Power and SMEMAX transformations. 4.Judging by the relative suitabilities of the Type III extremal distribution, Power and SMEMAX transformation, it was found that design low flows of all methods are closer to the observed data within 10 years of the return period and those of Power transformation can be acknowledzed as a reasonable one among others from the viewpoint of the median between values of Type m extremal distribution and SMEMAX transformation in addition to closing the observed than others over 10 years of the return period.

• Magazine of the Korean Society of Agricultural Engineers
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• v.32 no.E
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• pp.20-32
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• 1990

Abstract This study was conducted to pursue the normalization of frequency distribution by making an approach to the coefficient of skewness to nearly zero through the Box-Cox transformation, to get probable flood flows can be calculated by means of the transformation equation which has been derivated by Box-Cox transformation in the annual maximum series of the applied watersheds. It has been concluded that Box-Cox transfromation is proved to be more efficient than logarithmic, square root and SMEMAX transformation which is based on the trigonometric solution of a right triangle whose three verteces repesent the smallest, median and largest observed values of a population in making the coefficient of skewness nearer to zero. Consequently it is shown that probable flood flows according to the return period based on Box-Cox transformation are closer to the observed data as compared to other methods including SMEMAX transformation and fitted probability distributions such as the three parameter lognormal and the type I extremal distribution for the applied watersheds.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.4
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• pp.64-72
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• 1994

설계홍수량의 유도를 위해 일차적으로 극치계열인 금강, 영산강 및 석진강 수개 3개 유역의 연최고치계열을 중심으로 하여 SMEMAX법, 역변환(Power Transformation) 및 2단계역변환(Two step Power Transformation, TSPT)법에 의해 척도분포의 정규화를 위한 변환법의 효율성 검정과 설계홍수량의 유도 및 비교분석을 수행한 결과 SMEMAX 법과 Power 변환법에서는 정규분포화를 왜곡도계수의 영으로의 접근 시도는 가능하나 소설도, 3으로의 조건을 충족시킬 수 없었던 반면 2단계역변환법에서는 소설도, 3에 매우 근접된 결과를 가져오므로서 척도분포의 정규화를 기할 수 있었고 각각의 변환법에 유도된 설계홍수량간의 비교분석에서는 SMEMAX 및 Power 변환법에 비해 2단계역변환방법에 의한 설계 홍수량이 재현기간 10년 이상 실측치에 보다 접근된 좋은 결과를 나타내었다.

• KCID journal
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• v.5 no.1
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• pp.20-31
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• 1998

The Power transformation, the modified Power transformation, the logarithmic transformation, the square-root logarithmic transformation, the SMEMAX transformation, the Extreme value type III, the Weibull, the log Pearson type III, the lognormal distributi

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.5
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• pp.111-118
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• 1995

첨두유량이 연속적으로 발생하므로 인하여 수리구조물의 파괴에 영향을 끼치는 설계홍수량의 추정을 위해 본 연구에서는 제I보에 이어 2차적으로 부분 기간 계열인 금강, 영산강 및 섬진강 수계 6개 유역의 비년 초과치를 중심으로 하여 변환법인 SMEMAX법, 멱변화(Power Transformation) 및 2단계 멱변환(Two Step Power Transformation, TSPT)법에 의해 빈도분포의 정규화를 시도하고 이들에 대한 정규화 효율성의 비교분석과 설계홍수량 유도를 위한 변환법별 적합도 검정을 수행하였다. 왜곡분포의 정규화 시도는 제I보의 결과와 마찬가지로 SMAMAX 및 Power변환법에서는 빈도분포의 정규화가 미흡하였으나 2단계 멱변환법에서는 빈도분포의 만족한 정규화를 기할 수 있었다. 또한 3개 변환법에 의해 유도된 설계홍수량의 비교 분석에서는 3개 방법 모두 재현기간 20년 이내의 설계홍수량이 거의 유사한 결과를 나타내었으며 Kolmogorov-Smirnov Test에 의한 3개 변환법별 적합도검정 결과 2단계 멱변환법이 적정 변환법으로 인정되었다.