통계적 품질관리를 위한 왜도의 활용

김훈태,임성욱 한국품질경영학회 2023 품질경영학회지 Vol.51 No.4

Purpose: Skewness is an indicator used to measure the asymmetry of data distribution. In the past, product quality was judged only by mean and variance, but in modern management and manufacturing environments, various factors and volatility must be considered. Therefore, skewness helps accurately understand the shape of data distribution and identify outliers or problems, and skewness can be utilized from this new perspective. Therefore, we would like to propose a statistical quality control method using skewness. Methods: In order to generate data with the same mean and variance but different skewness, data was generated using normal distribution and gamma distribution. Using Minitab 18, we created 20 sets of 1,000 random data of normal distribution and gamma distribution. Using this data, it was proven that the process state can be sensitively identified by using skewness. Results: As a result of the analysis of this study, if the skewness is within ± 0.2, there is no difference in judgment from management based on the probability of errors that can be made in the management state as discussed in quality control. However, if the skewness exceeds ±0.2, the control chart considering only the standard deviation determines that it is in control, but it can be seen that the data is out of control. Conclusion: By using skewness in process management, the ability to evaluate data quality is improved and the ability to detect abnormal signals is excellent. By using this, process improvement and process non-substitutability issues can be quickly identified and improved. Purpose: Skewness is an indicator used to measure the asymmetry of data distribution. In the past, product quality was judged only by mean and variance, but in modern management and manufacturing environments, various factors and volatility must be considered. Therefore, skewness helps accurately understand the shape of data distribution and identify outliers or problems, and skewness can be utilized from this new perspective. Therefore, we would like to propose a statistical quality control method using skewness. Methods: In order to generate data with the same mean and variance but different skewness, data was generated using normal distribution and gamma distribution. Using Minitab 18, we created 20 sets of 1,000 random data of normal distribution and gamma distribution. Using this data, it was proven that the process state can be sensitively identified by using skewness. Results: As a result of the analysis of this study, if the skewness is within ± 0.2, there is no difference in judgment from management based on the probability of errors that can be made in the management state as discussed in quality control. However, if the skewness exceeds ±0.2, the control chart considering only the standard deviation determines that it is in control, but it can be seen that the data is out of control. Conclusion: By using skewness in process management, the ability to evaluate data quality is improved and the ability to detect abnormal signals is excellent. By using this, process improvement and process non-substitutability issues can be quickly identified and improved.

이익분포의 비대칭성이 분석가의 예측오차에 미치는 영향

강내철 ( Naechul Kang ),김길훈 ( Gilhoon Kim ) 한국회계학회 2015 회계학연구 Vol.40 No.4

본 연구는 분석가의 부주의나 고의가 없는 경우에도 이익분포가 비대칭이면 예측오차가 생길 수 있다는 관점을 제시한다. 분석가의 비용함수를 평균절대편차(Mean Absolute Error; MAE)를 최소화하는 것이라고 전제하면 분석가는 이익분포의 중간값을 예측치로 선택한다고 본다. 미래이익에 대한 최선의 기대치는 이익분포의 평균값인데 중간값을 예측치로 선택하면 의도하지 않은 예측오차가 생길 수 있다. 이 오차는 이익분포의 비대칭도에 비례하는 평균값과 중간값의 차이와 같다. 본 연구는 MAE를 최소화하기 위해 분석가가 이익분포의 중간값을 이익 예측치로 선택한다는 추론을 바탕으로 음(양)의 비대칭을 보이는 이익분포는 일정한 음(양)의 예측오차를 나타낼 것이란 예측을 규명한다. 이를 위해 최근 9년(2006년부터 2014년까지)의 분기이익 예측치를 분석하였다. 그 결과 이익분포의 비대칭도는 예측오차와 유의한 관련성을 나타낼 것이란 예측을 실증적 증거로 확인할 수 있었다. 이러한 분석결과는 예측오차에 영향을 미치는 다양한 요인들(기업규모, 분석가의 수, 적자여부, 이익예측의 불확실성, 최신 정보에 대한 분석가의 미온적 반응)의 효과를 통제한 후에도 유지되었다. 또한 이익분포의 비대칭도는 잠정실적 공시일의 주가반응과 음의 관계를 나타낸다는 사실을 확인하였다. 이것은 이익분포의 비대칭도가 클수록 주가반응이 둔화된다는 것으로 이익공시일의 비기대실적(earnings surprise) 중 비대칭성에서 기인한 부분을 상쇄하기 위한 주가조정이 나타난다는 것이다. 이것은 시장참여자들이 비대칭 이익분포와 관련된 예측오차의 문제를 어느정도 알고 있음을 의미한다. 본 연구는 MAE를 최소화하는 선택을 한다는 가정을 토대로 분석가 예측오차는 이익분포의 비대칭도와 일정한 상관관계를 가진다는 Gu and Wu(2003)의 연구가 계기가 되었다. 다만 그들의 연구에서 다루지 않았던 문제에 대한 추가적인 분석을 통해 추가적인 기여를 하였다고 할 수 있다. 본 연구에서는 분석가의 예측오차와 비대칭도의 관계를 보다 구체적인 상황에서 확인하기 위해 4/4분기의 이익비대칭과 예측오차 간의 관계를 부각하여 분석하였다. 그 결과 4/4분기에는 이익의 비대칭도가 다른 분기보다 더 커지는 한편 이익의 비대칭도가 예측오차에 미치는 영향이 증폭된다는 점을 확인하였다. This paper suggests that analysts`` optimal earnings forecasts can be biased without misbehavior nor selective behavior. If the analysts`` objective is to provide the forecast minimizing the mean absolute forecast error (MAE), the optimal forecast is the median rather than the mean earnings. The earnings distributions of firms are mostly skewed for a variety of reasons. Thus, if analysts forecast the median earnings to achieve minimum MAE, their forecasts are biased by the mean-median differences of the earnings distributions. In this paper, we are assured that there are a significantly positive relation between earnings skewness and analyst forecast bias. These findings are robust after controlling for various other factors proposed in previous studies; such as size, analyst following, losses or gains, uncertainty in earnings forecasts, selection bias, analysts under-reaction, and analysts`` incentives to generate trading commissions. We also find some evidence that the stock market response to earnings announcement is positively related with analysts`` forecast error and negatively related with earnings skewness. This means that stock market understands part of the skewness-induced bias and is able to adjust accordingly. The findings in this paper complement the existing explanations of analyst forecast bias. In addition, this explanation makes several contributions to the literature. First, while most existing theories are explicitly motivated by explaining only analyst forecast optimism, the explanation in this paper applies to both forecast optimism and pessimism. The selection bias explanation supports only forecast optimism. The selection bias explanation argues that analysts may censor their forecasts when the prospects of the firm are unfavorable, leading to optimism in the observed forecasts. This implies that those unobservable forecasts which analysts choose to drop or not cover may be pessimistic. The explanation in this paper suggests that systematic pessimism could exist in the observed forecasts for firms that analysts do cover. In particular, absent other factors, positively skewed earnings would lead to forecast pessimism. It can also be noted that analysts`` under-reaction to good news could result in forecast pessimism, though most studies focus on under-reaction related optimism in the face of bad news. Second, in addition to explaining the cross-sectional variations in forecast bias, earnings skewness has implications for explaining other observed patterns in analyst forecast bias. For example, Basu et al.(2005) document that analyst forecasts are more optimistically biased for the fourth quarter earnings than for other quarterly earnings. One possible explanation is that earnings are more negatively skewed in the fourth quarter than in other quarters. There does seem to be some support for these explanations. We found that skewness measures are more negative for the fourth quarter earnings than for other quarterly earnings and have become less negative over the more recent years in our sample period. Third, it can be true that the market appears to understand part of the skewness induced forecast bias. The literature so far has generally suggested that the market is rather fixated on analysts`` biased forecasts, with findings of predictable patterns in abnormal returns similar to those in analyst forecast errors. This is inconsistent with the implications of an efficient market. Since skewness-induced bias is based on analysts`` rational behavior, We expect the investors to understand such behavior and make appropriate adjustments. Further study of market efficiency would benefit from differentiating the sources of analyst forecast biases. This article is replication of Gu and Wu(2003)``s research inasmuch as we also discuss the relation between analysts`` forecast bias and skewness of earnings distribution based on assumption that analysts choose the forecasts of minimum MAE. We tried to differentiate this article from theirs and contribute by appending additional discuss on ferecast bias of 4/4 quarter. We examine the relation between analysts`` forecast bias and skewness in earnings distribution focussing in 4/4 quarter for analyzing the relation in more specific situation. Thus we can find that the skewness of earnings distribution in 4/4 quarter is larger than that of other quarter and that an impact of the skewness of earnings distribution on analysts`` forecast bias is amplified in 4/4 quarter.

Multi-Dependent Criteria Supplier Selection with Uncertain Performance Evaluation

O. Anuchitchanchai,K. Suthiwartnarueput,P. Pornchaiwiseskul 인하대학교 정석물류통상연구원 2018 JOURNAL OF INTERNATIONAL LOGISTICS AND TRADE Vol.16 No.2

Nowadays businesses tend to compete with rivals by improving capability to meet customer demands. One of the key to improve logistics efficiency of a firm is to select appropriate supplier. In the past, to select the most suitable supplier, most people evaluated performance by using average performance or variance from historical data but did not mentioned skewness. In other words, skewness impact on supplier performance is ignored by researchers and buyers. In fact, supplier with greatest average performance does not confirm to be the most suitable one because of uncertainties which make its performance skew either to the left or right, i.e., lower or higher than expectation. Therefore, this empirical study aims to discover and determine the important role of skewness on supplier selection problem. After identifying influential criteria on supplier selection, we analyze skewness effect on suppliers’ performance in each criterion by surveying real data of suppliers’ performances. Skewness effect can be rated in 3 levels; no effect, moderately effect, and highly effect. The results show that, there is only one criterion with no skewness effect, which is price. Criteria which have high skewed performance, for both of medium-sized and large-sized buyers, are lead time, product quality and reliability, and on-time delivery. Also, skewness has higher effect on suppliers’ performance of medium-sized buyers than large-sized buyers. The conclusion surprisingly shows that, skewness is the best index to distinguish between good and bad suppliers, while mean is the worst index.

Skewness Preference and IPO Underpricing : International Evidence

Eunyoung Cho,Woojin Kim 한국재무학회 2020 한국재무학회 학술대회 Vol.2020 No.08

This paper examines the impact of expected skewness on IPO underpricing based on a comprehensive set of 17,051 IPOs from 23 countries between 1990 and 2013. We find that IPOs with high expected skewness have significantly higher first-day return around the world, confirming the previous results based on U.S. IPOs. Such preference for skewness remains robust to estimation method or portfolio formation and is more pronounced in countries with relatively higher gambling propensity, a larger number of non-religious populations, and more individualistic culture. Finally, IPOs with high expected skewness underperform those with low expected skewness. Our results provide additional empirical support for skewness preference and pricing of lottery type assets in an international setting.

Multivariate measures of skewness for the scale mixtures of skew-normal distributions

Kim, Hyoung-Moon,Zhao, Jun The Korean Statistical Society 2018 Communications for statistical applications and me Vol.25 No.2

Several measures of multivariate skewness for scale mixtures of skew-normal distributions are derived. As a special case, those of multivariate skew-t distribution are considered in detail. Furthermore, the similarities, differences, and behavior of these measures are explored for cases of some specific members of the multivariate skew-normal and skew-t distributions using a simulation study. Since some measures are vectors, it is better to take all measures in the same scale when comparing them. In order to attain such a set of comparable indices, the sample version is considered for each of the skewness measures that are taken as test statistics for the hypothesis of t distribution against skew-t distribution. An application is reported for the data set consisting of 71 total glycerol and magnesium contents in Grignolino wine.

Reliability study on skewness of doublet impinging injectors

Bimal Subedi,손민,장석필,구자예 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.5

The atomization characteristics of skewed like-on-like impinging injectors were studied using water as a simulant. The shadowgraph technique and Laser deflection analyzer were used to understand the variances in spray mode, breakup length, and spray angles with the fraction of skewness under different angles of impingement, pressure, and Weber number. The range of reliability of performance from the perspective of the manufacturer was determined through quantitative and qualitative analyses of atomization and spray characteristics. The three different modes of spray breakup were well mixed, reflective, and transmissive. The breakup length decreased with the increase in spray angle up to a certain fraction of skewness. The spray fan angle and SMD in skewed impinging injection were directly proportional to the fraction of skewness. A large fraction of skewness provided the spray sheet with a small droplet size at the center of the spray sheet and large droplet sizes with rising radial distances toward the edge of the sheet. This paper attempts to define the maximum allowable misalignment and basic reliability limit for the design and evaluation of performance of impinging injectors in terms of fraction of skewness. Values at the perfect impingement condition were used as references for the significant reduction in the manufacturing cost of impinging injectors.

변동성, 왜도, 첨도와 주식수익률의 횡단면

심명화 한국재무관리학회 2016 財務管理硏究 Vol.33 No.1

I compute historical volatility, skewness, and kurtosis for individual stock returns and investigate a cross-sectional relation between each moment and stock returns. First, I find that skewness is negatively related to subsequent stock returns, where skewness is estimated using 30-day, 60-day, and 180-day windows. The relation remains significant after controlling for various cross-sectional effects such as size, book-to-market, and short-term return reversals. Second, I find that the negative relation between skewness and future stock returns is more negative and significant among stocks that are heavily traded by individual investors. This evidence suggests that a preference for skewness or lottery-type stocks is the source of the negative skew-return relation, given that individual investors more likely to have a greater gambling propensity. Third, I find the skewness-return relation becomes less significant with a longer estimation window. It may highlight the possibility that skewness measures computed from short- and recent-period data are likely to contain different information from those computed from long-period data. Lastly, I find a positive relation between kurtosis and subsequent stock returns, where kurtosis is computed using 1-year and 2-year estimation windows. 본 연구는 국내 주식시장에서 수익률 변동성(volatility), 왜도(skewness), 첨도(kurtosis)와 수익률과의 횡단면적 관계를 살펴보고, 나아가 각 적률의 추정기간에 따라 수익률과의 관계가 달라지는지 분석한다. 주요 발견은 다음과 같다. 첫째, 단기에서 추정한 왜도가 높은 주식일수록 평균수익률이 낮다. 기업규모, 장부가치 대 시장가치비율, 단기 수익률 반전 등 수익률과 관련이 있다고 알려진 여러 기업특성을 통제하고도 유의하다. 둘째, 단기 왜도와 수익률의 음의 관계는 개인투자자 거래 비중이 높은 주식들 중에서 더 두드러진다. 왜도와 수익률의 관계가 개인투자자의 고왜도 선호에 기인함을 지지하는 결과이다. 셋째, 장기에서 왜도를 추정한 경우 왜도와 수익률의 음의 관계는 더 이상 유의하지 않다. 이는 단기 왜도와 장기 왜도에 내포된 정보가 서로 다를 가능성을 시사한다. 넷째, 장기에서 추정한 첨도는 수익률과 양의 관계에 있다. 투자자들의 첨도 회피 가설과 일관된 결과로 다른 기업 특성들을 통제하고도 유의하게 나타났다. 마지막으로, 변동성과 수익률의 음의 관계는 변동성의 추정 기간에 관계없이 유의하다.

대환기로 편성한 싱글 져지 대환편성물의 사행도에 관한 연구. II. 사행도의 최소화 방법과 응용

박찬호,김주용,심현주,Park, Chan Ho,Kim, Jooyong,Shim, Hyunjoo 한국섬유공학회 2015 한국섬유공학회지 Vol.52 No.4

In a previous work, the causes of skewness in single jersey fabric produced on a circular knitting machine were analyzed from two aspects, namely, the machine characteristics and the yarn torsional properties. For practical reasons, the skewness caused by the machine (feeding skewness) could not be reduced, thus making it necessary to control the yarn torsion. One way of counterbalancing the yarn torsion was to alternately feed the S- and Z-twisted yarns into the knitting machine, while another method relied on using S- and Z-twisted single yarns plied together and fed through the same feeder. The results showed that a knit fabric made using plied yarn could reduce skewness. However, the hand is hard and not appropriate for this purpose. The method relying on the combined feeding of S- and Z-twisted yarn could improve the skewness while producing a pleasant touch and appearance. Nevertheless, production costs should be considered. Finally, the method relying on the alternate feeding of S- and Z-twisted yarn produced no skewness. Unfortunately, however, the fabric had a harsh appearance and was unpleasant to the touch. Taking the production costs and fabric properties into account, the use of steam set yarn is thought to offer the most practical solution.

Test of Sectoral Shifts Hypothesis Based on Robust Measures of Dispersion and Skewness

Yanggyu Byun(변양규),Joo-Young Jeon(전주영) 한국노동연구원 2010 노동정책연구 Vol.10 No.2

‘부문간 노동이동 가설(Sectoral Shifts Hypothesis)’에 의하면 경제 전체에 대한 충격이 없는 경우라도 산업간 노동이동에 의해 실업률이 크게 변동할 수 있다. Lilien(1982)을 포함한 모든 과거 연구들은 우선 각 산업의 순고용률(net hiring rate)에서 경기변동의 영향을 제거한 부문별 충격 분포(sectoral shock distribution)를 추정하고 이로부터 전통적인 방식의 분산 및 왜도(classical measures of dispersion and skewness)를 계산하여 부문간 노동이동의 정도를 파악하였다. 그러나 이러한 분산 및 왜도는 이상치(outlier)에 대해 상당히 민감하게 반응하며 그결과 ‘부문간 노동이동 가설’에 대한 검증 역시 이상치에 의해 왜곡될 수 있다는 지적이 있다. 본 연구의 결과에 의하면 우선 부문별 충격의 분포에는 상당한 정도의 이상치가 존재하는 것으로 나타났으며 그 결과 전통적 방식에 의해 계산된 분산 및 왜도를 이용할 경우 검증 결과가 왜곡될 가능성이 있는 것으로 추정된다. 이러한 결과에 근거해 본 연구는 다양한 형태의 강건분산 및 강건왜도(robust measures of dispersion and skewness)를 활용하여 미국의 1955년 이후 노동시장에 대한 ‘부문간 노동이동 가설’을 검증하였다. 검증 결과에 의하면 강건분산 및 강건왜도로 측정된 부문간 노동이동은 여전히 실업률 결정에 상당히 유의한 영향을 미치는 것으로 나타났다. 특히 실업률 변동 중 부문간 노동이동으로 설명되는 자연실업률 부분이 49~68%나 됨에 따라 기존 총수요 관리정책을 통한 실업률 안정화정책의 역할은 상당히 제한적이며 오히려 부문간 노동이동을 원활히 하는 정책이 실업률 안정화에 효과적일 수 있다는 함의를 얻을 수 있다. Sectoral shifts hypothesis states that sectoral reallocation of labor demand has a significant effect on the fluctuation of unemployment rate even in the absence of aggregate shocks. Many studies have found strong evidence supporting the hypothesis. In those studies, classical measures of dispersion and skewness of the cross-sectional distribution of estimated sectoral shocks have been used to represent the effect of sectoral shifts on aggregate unemployment rates. However, it is well known that classical measures of moments are strongly affected by the presence of outliers. Consequently, the test of sectoral shifts hypothesis can be distorted by the presence of a few outliers. This paper examines the presence of outliers in the sectoral shocks estimated from the U.S. industrial data, and tests the sectoral shifts hypothesis based on alternative robust measures of the dispersion and skewness. We find strong evidence of the presence of outliers. However, it turns out that sectoral shifts hypothesis is still strongly supported when robust measures of dispersion and skewness are used as a measure of sectoral shifts. We also find that even in the absence of aggregate shocks the natural rate of unemployment fluctuates significantly over time due to sectoral shifts.

Asymmetric Correlation as an Explanation for the Effect of Asset Skewness on Equity Returns

Y. Peter Chung,Thomas S. Kim 한국증권학회 2017 Asia-Pacific Journal of Financial Studies Vol.47 No.5

Assets with asymmetric correlation tend to cause portfolios to have negative skewness. We develop measures of asymmetric correlation based on portfolio skewness. We find that asymmetric correlation is better measured with the skewness of smaller portfolios. The skewness of individual-stock returns has the most significant and consistent explanatory power for stock returns, indicating that asymmetric correlation is generated at the asset level of individual firms.