A class of ratio distributions of dependent folded normals and its applications

Abstract

If U has a normal distribution, then $|U|$ is said to have a folded normal distribution. The distribution can be viewed as one involving normal measurements without their algebraic sign. As a natural extension of the distribution, we propose a distribution of the ratio of two correlated folded normals and demonstrate its statistical applicability by considering some properties of the distribution. Necessary theories on the expectation of a function of $|U|$ are provided to derive the properties. Likelihood inference for the proposed distribution is developed, and a simulation study is implemented to verify the inference. Further, four examples are presented to illustrate the practical application of the distribution.

Keywords:

• exact distribution
• inference
• properties
• ratio of folded normals
• unsigned data

MSC 2010 Classification:

• 62E15
• 62F10
• 62P20

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2013R1A2A2A01004790).