A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator

Authors

  • K. N. Radhalakshmi Loyola College
  • M.L. William Loyola College

DOI:

https://doi.org/10.6092/issn.1973-2201/12336

Keywords:

Kurtosis, Moment estimators, Non-mesokurtic distributions

Abstract

In a good number of real life situations, the observations on a random variable of interest tend to concentrate either too closely or too thinly around a central point but symmetrically like the normal distribution. The symmetric structure of the density function appears like that of a normal distribution but the concentration of the observations can be either thicker or thinner around the mean. This paper attempts to generate a family of densities that are symmetric like normal but
with different kurtosis. Drawing inspiration from a recent work on multivariate leptokurtic normal distribution, this paper seeks to consider the univariate case and adopt a different approach to generate a family to be called ’univariate non-mesokurtic normal’ family.The symmetricity of the densities is brought out by a uniform random variable while the kurtosis variation is brought about by a chi generator. Some of the properties of the resulting class of distributions and the pameter estimation are discussed.

References

J. M. AREVALILLO, H.NAVARRO (2012). A study of the effect of kurtosis on discriminant analysis under elliptical populations. Journal of Multivariate Analysis, 107, pp. 53–63.

L. BAGNATO, A. PUNZO, M. G. ZOIA (2017). The multivariate leptokurtic-normal distribution and its application in model-based clustering. Canadian Journal of Statistics, 45, no. 1, pp. 95–119.

K. P. BALANDA, H.MACGILLIVRAY (1988). Kurtosis: a critical review. The American Statistician, 42, no. 2, pp. 111–119.

K. P. BALANDA, H. L. MACGILLIVRAY (1990). Kurtosis and spread. Canadian Journal of Statistics, 18, no. 1, pp. 17–30.

S. CAMBANIS, S. HUANG, G. SIMONS (1981). On the theory of elliptically contoured distributions. Journal of Multivariate Analysis, 11, no. 3, pp. 368–385.

K. V. MARDIA (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, no. 3, pp. 519–530.

G. P. SZEGÖ (2004). Risk measures for the 21st century, vol. 1. Wiley New York.

J.WANG,W. ZHOU (2012). A generalized multivariate kurtosis ordering and its applications. Journal of Multivariate Analysis, 107, pp. 169–180.

Downloads

Published

2021-10-26

How to Cite

Radhalakshmi, K. N., & William, M. L. (2021). A Class of Univariate Non-Mesokurtic Distributions Using a Continuous Uniform Symmetrizer and Chi Generator. Statistica, 81(2), 217–227. https://doi.org/10.6092/issn.1973-2201/12336

Issue

Section

Articles