In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta(𝑎,1)(a,1) distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher’s information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions.
Keywords:
Gleser distribution; heavy-tailed distribution; maximum likelihood; scale mixture
MSC: 62E15; 62E20