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Descriptive and predictive analytics of agricultural data using machine learning algorithms
Published in Govind Singh Patel, Amrita Rai, Nripendra Narayan Das, R. P. Singh, Smart Agriculture, 2021
Kurtosis is the method to find the outliers in the sequence of data. This can be divided into high and low kurtosis. If the kurtosis is high, the data are having high amount of outliers. It should be considered for further processes. If the kurtosis is low, then the data are having low outliers. Based on the value of kurtosis, it can be classified into following three types: Mesokurtic: The kurtosis of the distribution is same as the normal distribution value.Leptokurtic: If kurtosis > 3, then it is high than the mesokurtic which means the data contains high outliers.Platykurtic: If kurtosis < 3, then it is meant by shorter distribution and data are having low level of outliers (Kumar and Choudhry 2010).
Signal Quality Assessment
Published in Mohamed Elgendi, PPG Signal Analysis, 2020
Recently, Selvaraj et al.[75] found that kurtosis is a good indicator for PPG signal quality. Kurtosis is a statistical measure used to describe the distribution of observed data around the mean. It represents a heavy tail and peakedness, or a light tail and a flatness of a distribution relative to the normal distribution, which is defined as: KSQI=1/N∑i=1Nxi−μ̂x/σ4 where μ̂x and σ are the empirical estimate of the mean and standard deviation of xi, respectively; and N is the number of samples in the PPG signal. A MATLAB function can be used as follows:
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.
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.
Performance evaluation of Weibull analytical methods using several empirical methods for predicting wind speed distribution
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
The kurtosis is used to measure the departures of data from normal distribution characteristics. Kurtosis measures the shape of distribution (DeCarlo 1997) apart from the turbulence intensity that represents the magnitude of quantity to wind fluctuation (Lemes, Guetter, and Andrade 2017). Kurtosis is defined as normalized fourth-order moments minus three that yielding either to zero, having a normal distribution property or excess kurtosis coefficients as expressed in Equation (8). The excess kurtosis coefficients (Kurt) can be positive or negative to present a heavy or light and peakedness or flatness, respectively (Gravetter and Wallnau 2014). According to Manwell (Manwell, McGowan, and Rogers 2010), Turbulence Intensity (TI) indicated to be on the low level when the ratio of standard deviation and average wind speed is less than 0.1; moderate level from 0.1 to 0.25, and high level when is greater than 0.25. The TI is expressed in Equation (9).