On the asymptotic distribution of an alternative measure of kurtosis

  • Authors

    • Kagba Suaray California State University Long Beach
    2015-08-07
    https://doi.org/10.14419/ijasp.v3i2.5007
  • Kurtosis, Quantile Estimator, Ratio of Normal Variables, Spread Function.

  • Abstract

    Pearson defined the fourth standardized moment of a symmetric distribution as its kurtosis. There has been much discussion in the literature concerning both the meaning of kurtosis, as well as the effectiveness of the classical sample kurtosis as a reliable measure of peakedness and tail weight. In this paper, we consider an alternative measure, developed by Crow and Siddiqui, used to describe kurtosis. Its value is calculated for a number of common distributions, and a derivation of its asymptotic distribution is given. Simulations follow, which reveal an interesting connection to the literature on the ratio of normal random variables.

  • References

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  • Received date: 2015-06-29

    Accepted date: 2015-07-23

    Published date: 2015-08-07