A Generalization of the Univariate Slash by a Scale-Mixtured Exponential Power Distribution

Abstract

A generalization of the slash distribution is derived using the scale mixture of the exponential power distribution. The newly defined family of distributions provides a rich flexibility on the tail heaviness and yields alternative robust estimators of location and scale in non normal situations. In order to investigate asymptotically the bias properties of the estimators, a simulation study is performed. The performance of the estimators on two well-known real data sets is also illustrated.

Keywords:

• Exponential power distribution
• Heavy tail
• M-estimation
• Robustness
• Slash distribution

Mathematics Subject Classification:

• Primary 62F35
• Secondary 62F10