• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.463-475
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• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.423-435
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• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• Journal of Electrical Engineering and Technology
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• v.12 no.5
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• pp.1955-1962
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• 2017

Induction motors are a workhorse for the industry. The condition monitoring and fault analysis are the main concern for the engineers. The bearing is one of the vital segment of the induction machine and the condition of the whole machine is decided based on the condition of the bearing. In the present paper, the vibration signal of the bearing has been used for the analysis. The first line of action is to perform a statistical analysis of the vibration signal which gives trends in signal. To get the location of a fault in the bearing the second action is to develop an index based on Wavelet Packet Transform node energy named as Bearing Damage Index (BDI). Further, Teager-Kaiser Energy Operator (TKEO) has been calculated from higher index value to get the envelope and finally Power Spectral Density (PSD) has been applied to identify the fault frequencies. A performance index has also been developed to compare the usefulness of the proposed method with other existing methods. The result shows that the strong amplitude of fault characteristics and its side bands help to decide the type of fault present in the recorded signal obtained from the bearing.

• Journal of The Korean Astronomical Society
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• v.53 no.2
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• pp.49-57
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• 2020

We present numerical simulations of decaying hydrodynamic turbulence initially driven by solenoidal (divergence-free) and compressive (curl-free) drivings. Most previous numerical studies for decaying turbulence assume an isothermal equation of state (EOS). Here we use a polytropic EOS, P ∝ ρ^γ, with polytropic exponent γ ranging from 0.7 to 5/3. We mainly aim at determining the effects of γ and driving schemes on the decay law of turbulence energy, E ∝ t^-α. We additionally study probability density function (PDF) of gas density and skewness of the distribution in polytropic turbulence driven by compressive driving. Our findings are as follows. First of all, we find that even if γ does not strongly change the decay law, the driving schemes weakly change the relation; in our all simulations, turbulence decays with α ≈ 1, but compressive driving yields smaller α than solenoidal driving at the same sonic Mach number. Second, we calculate compressive and solenoidal velocity components separately and compare their decay rates in turbulence initially driven by compressive driving. We find that the former decays much faster so that it ends up having a smaller fraction than the latter. Third, the density PDF of compressively driven turbulence with γ > 1 deviates from log-normal distribution: it has a power-law tail at low density as in the case of solenoidally driven turbulence. However, as it decays, the density PDF becomes approximately log-normal. We discuss why decay rates of compressive and solenoidal velocity components are different in compressively driven turbulence and astrophysical implication of our findings.

• The Journal of the Korea Contents Association
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• v.21 no.11
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• pp.320-332
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• 2021

This paper investigates the influence of stock-level left-tail risk, which is defined using Value-at-Risk(VaR) estimates of past one-year daily stock returns, in the expected stock returns in the Korean stock market. Our results are summarized as follows: First, monthly-constructed zero-cost portfolios that buy (shortsell) the highest (lowest) left-tail risk decile in the previous month exhibit an average monthly return (called left-tail risk premium) of -2.29%. Second, Fama-MacBeth cross-sectional regressions suggest that left-tail risk in the previous month shows significant and negative explanatory power over return in this month, after controlling for various firm characteristics such as firm size, B/M, market beta, liquidity, maximum daily return, idiosyncratic volatility, and skewness. Third, the stocks with larger recent month loss have lower returns in the next month. Fourth, the magnitude of left-tail risk premium is negatively related with lagged market-level volatility. These results support the hypothesis from a perspective of behavioral finance that the overpricing of stocks with left-tail risk is attributed to the investors' underreaction to it.