Exponentiated Sinh Cauchy Distribution with Applications

• Activity Number: 249
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Kahadawala Cooray*+
• Companies: Central Michigan University
• Keywords: Bimodal and unimodal data ; Cauchy distribution ; Hyperbolic secant distribution

Abstract

The exponentiated sinh Cauchy distribution is characterized by four parameters: location, scale, symmetry, and asymmetry. The symmetric parameter preserves the symmetry of the distribution by producing both bimodal and unimodal densities having coefficient of kurtosis values range from one to positive infinity. The asymmetric parameter changes the symmetry of the distribution by producing both positively and negatively skewed densities having coefficient of skewness values range 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 symmetric and asymmetric parameter plane. The maximum likelihood parameter estimation technique is discussed, and examples are provided, analyzed, and compared based on data from environmental sciences to illustrate the flexibility of the distribution for modeling bimodal and unimodal data.