Exponentiated Sinh Cauchy Distribution with Applications

Abstract

The exponentiated sinh Cauchy distribution is characterized by four parameters: location, scale, symmetry, and asymmetry. The symmetry parameter preserves the symmetry of the distribution by producing both bimodal and unimodal densities having coefficient of kurtosis values ranging from one to positive infinity. The asymmetry parameter changes the symmetry of the distribution by producing both positively and negatively skewed densities having coefficient of skewness values ranging from negative infinity to positive infinity. Bimodality, skewness, and kurtosis properties of this regular distribution are presented. In addition, relations to some well-known distributions are examined in terms of skewness and kurtosis by constructing aliases of the proposed distribution on the symmetry and asymmetry parameter plane. The maximum likelihood parameter estimation technique is discussed, and examples are provided and analyzed based on data from astronomy and medical sciences to illustrate the flexibility of the distribution for modeling bimodal and unimodal data.

Keywords:

• Bimodal and unimodal data
• Cauchy distribution
• Hyperbolic secant distribution

Mathematics Subject Classification:

• Primary 62Exx
• Secondary 62E10, 62P10, 62P35

Acknowledgments

I am grateful for the valuable suggestions of the editor and referees. Their insightful and constructive comments have substantially enhanced this article.

Notes

‡ λ value in parenthesis produces the same kurtosis for each distribution.