A New Familiy of Skewed Slash Distributions Generated by the Cauchy Kernel

Abstract

The present study introduces a new family of univariate skewed slash distributions generated by the Cauchy kernel, which arise as the ratio of skewed distributions generated by the Cauchy kernel and independent uniform power function distributions. Skewed Slash distributions generated by the Cauchy kernel were derived and the properties of the resulting distributions were studied. Cauchy and slash Cauchy distributions are special cases of this new family. These distributions provide us alternative choices in simulation study and in particular, in fitting skewed data sets with heavy tails. Finally, some possible applications of the models are discussed.

Keywords:

• Cauchy distribution
• Slash Cauchy distribution
• Slash skew Cauchy-Cauchy distribution
• Slash skew Cauchy-Laplace distribution
• Slash skew Cauchy-Normal distribution

Mathematics Subject Classification:

• 62E15
• 62N02
• 62P10

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Erratum

Acknowledgment

The author is grateful to the Department of Science & Technology, Government of India, New Delhi, for financial support under the Women Scientist Scheme (WOS-A (2008)), Project No: SR/WOS-A/MS-09/2008.