On the Ratio of Two Folded Normal Distributions

Abstract

A class of distributions associated with the ratio of two folded normal random variables is introduced which strictly includes the half standard Cauchy distribution. The properties of this class of distributions are studied, along with a graph of the possible shapes of its density functions. The salient features of this class are mathematical tractability and statistical applicability. Utility of the class of distributions is demonstrated by presenting four applications.

Keywords:

• Distributional properties
• Doubly non central distributions
• Ratio of folded normals
• Unsigned data

Mathematics Subject Classification:

• 62E15
• 62F10

Acknowledgments

The author would like to thank the referees and the associate editor for their careful reading of the manuscript and for suggestions which improved the presentation of this article.