China
Africa
Explore chapters and articles related to this topic
Statistical Analysis of Random Dynamic Responses of Bridge under Dense Traffic Flow
Published in Jian Zhang, Zhishen Wu, Mohammad Noori, Yong Li, Experimental Vibration Analysis for Civil Structures, 2020
Linfeng Hu, Jiayan Lei, Wei Shi, Zihao Wang
The kurtosis-skewness test is used to study whether the acceleration follows the law of normal distribution. The skewness of distribution is a measure of symmetry, and the kurtosis is a measure of peakedness. The standard normal distribution has a skewness value of 0 and a kurtosis value of 3. Thinking that response of environmental excitation conforms to the Gaussian white noise assumption, there must be an acceleration interval in which the statistical distribution of acceleration obeys the standard normal distribution. According to the theory of kurtosis-skewness test, it can be considered that the absolute value of the acceleration when the kurtosis value of environmental excitation is 3 is the demarcation point between the two parts of responses. In order to test this hypothesis, the original acceleration data is divided into two groups, and the kurtosis-skewness method is used to determine the normality of the acceleration distribution. The acceleration data of measuring point 1-1 is collected, and the boundary acceleration when the kurtosis value is 3 is obtained is shown in Table 33.1.
Statistics, probability and probability distributions
Published in Stephen A. Thompson, Hydrology for Water Management, 2017
Figures 3.1a–c are examples of three different probability distributions. Figure 3.1b shows a distribution with no skewness, or more accurately, the skewness is equal to zero. Data with negligible skewness are normally distributed. Figure 3.1b is an example of a normal distribution, while Figures 3.1a and 3.1c are other probability distributions. The term normal is used to describe symmetrical, bell-shaped distributions, and does not mean that the other distributions are somehow abnormal, though they certainly are non-normal. One way to eliminate skewness is to logarithmically transform the data as done in Section 2.6. The reason for normalizing data is so that we can use normal-distribution statistical techniques. We will see in Chapter 11 that certain methods of flood frequency analysis use logarithmically-transformed data.
Miscellaneous application of chemometrics
Published in Madhusree Kundu, Palash Kumar Kundu, Seshu Kumar Damarla, Chemometric Monitoring: Product Quality Assessment, Process Fault Detection, and Applications, 2017
Madhusree Kundu, Palash Kumar Kundu, Seshu Kumar Damarla
The ECG signal is a nonstationary one (with bursts like QRS features contributing a localized high-frequency component) that can be ascertained by simple and preliminary measures like covariance, skewness, kurtosis, and autocorrelation function (ACF) of the ECG signal. Skewness is a measure of symmetry, or more precisely, the lack of symmetry in data distribution. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or a lack of outliers. Many classical statistical tests and intervals depend on normality assumptions. Significant skewness and kurtosis clearly indicate that the data are not normal. If a data set exhibits significant skewness or kurtosis, some transformation can be applied to make the data normal. Another approach is to use techniques based on distributions other than normal. Figures 7.6 through 7.9 present the kurtosis, covariance, skewness, and ACF present in the MI inferior ECG data revealing the nonstationary aspect present in the ECG signal. The programs required to determine the previously mentioned time series features of ECG data follow.
Comparative analysis of deep learning and classical time series methods to forecast natural gas demand during COVID-19 pandemic
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2023
Table 2 presents the descriptive statistical analysis of the 2-year average weekly natural gas consumption since the beginning of the epidemic. The mean and standard deviation of the 105-week natural gas consumption data were found to be 158.068 and 52.056 million Sm3, respectively. These statistics are useful for understanding the central tendency and variability of the data. Additionally, standardized skewness and kurtosis values were calculated to determine whether the dataset conforms to a normal distribution. Skewness refers to the degree of symmetry in the distribution, while kurtosis measures the degree of peakedness or flatness of the distribution compared to a normal distribution. The standardized skewness and kurtosis values were found to be 1.063 and −1.988, respectively. These values fall within the expected range of −2 to + 2 for a normal distribution. Therefore, it can be concluded that the distribution of the natural gas consumption data is approximately normal.
Atlas of surface currents in the Mediterranean and Canary–Iberian–Biscay waters
Published in Journal of Operational Oceanography, 2022
Justino Martínez, Emilio García-Ladona, Joaquim Ballabrera-Poy, Jordi Isern-Fontanet, Sergio González-Motos, José Manuel Allegue, Cristina González-Haro
Skewness and kurtosis provide a first estimate of how much a given distribution deviates from the normal one. Kurtosis is sensitive to departures from normality on the tails, whereas skewness provides information about how much the overall shape of a distribution deviates from the normal one. It reflects the asymmetry of the distribution function. For large enough sample sizes (typically larger than 300), it is acceptable to consider the distribution does not deviate much from a normal univariate distribution if the skewness lies in the range [−2:2] and the absolute kurtosis is lower than 7 (West et al. 1995; Kim 2013). The data sets used to perform this study cover 27 years for GLOBCURRENT and SEALEVEL products and 33 years for MEDSEA product. Moreover, the MEDSEA climatology has been computed at a resolution 3 times coarser than the original product and the number of available values to compute the climatology at each point and for each month is 9 times larger. This number is slightly reduced due to the outliers detection performed on all products, but for each distribution, it mainly moves in the range 650–800 for GLOBCURRENT and SEALEVEL products, and 7500–9000 for MEDSEA product, long exceeding the mentioned limit of 300 measures and the normality test can be applied without the need to resort to z-test, K–S tests or Q–Q plots. Only small deviations from normality are observed for the three data sets described in Table 1.
Effects of exercise intensity on anticipation timing performance during a cycling task at moderate and vigorous intensities in children aged 7–11 years
Published in European Journal of Sport Science, 2020
Ruth Boat, Martyn Morris, Michael J. Duncan
Each participant’s raw scores across each of the stimulus speeds were summarised into three error scores as a way of generating the dependent variables. This is consistent with previous recognised protocols using CAT (Duncan et al., 2013; Duncan et al., 2015; Isaacs & Pohlman, 1991; Lyons et al., 2008; Sanders, 2011). First, constant error represents the temporal interval (milliseconds) between the arrival of the visual stimulus and the end of the participant’s motor response. It signifies the mean response of the participant and the direction of error (i.e. early or late). Second, a variable error was the participant’s standard deviation from their mean response and symbolises the variability/inconsistency of responses (Lyons et al., 2008). However, as variable error signifies the standard deviation from the mean, the data are positively skewed (all the values are positive). Therefore, the data set were log transformed as log-transforming data in this way has been shown to overcome skewness in previous work (Lyons et al., 2008). Third, an absolute error was the value of each raw score discounting whether the response was early or late. The absolute error provides the best depiction of both the individual and combined effects of task characteristics as a whole (Sanders, 2011), and therefore represents the most popular reported CAT outcome variable within the literature (Lyons et al., 2008; Sanders, 2011). Similar to variable error, the data for absolute error were skewed, therefore the data was log transformed akin to previous research (Lyons et al., 2008).