An Alternative Measures of Moments Skewness Kurtosis and JB Test of Normality

Abstract

If we know the statistics of central tendency and dispersion, we still cannot nature a complete design about the distribution. About these measures we should know more information's of skewness and kurtosis, which are enables us to have a design the distribution. However, there is evidence that they may response poorly in the presence of non-normality or when outliers arise in data. We examine the performances of popular and frequently used measures of skewness β1, kurtosis β2 and Jarque–Bera test of normality that they may not perform and we anticipates in the existence of non-normality or outliers. In this paper, firstly, we develop robust measures of moments and we formulate a new statistics of skewness and kurtosis which we name robust skewness ϕ1 and robust kurtosis ϕ2. Again, in this paper, we modify Jarque–Bera test of normality, which we label Robust Jarque–Bera (RJB). These measures should be fairly robust. The effectiveness of the proposed measures is investigated by simulation approach. The results demonstrate that the newly proposed skewness ϕ1, kurtosis ϕ2 and RJB test outperform the skewness, kurtosis and Jarque–Bera test of normality when a small percentage of outliers are present or absent in the data.

Keywords

• Robust moments
• Robust skewness
• Robust Kurtosis
• Robust test of normality