General results for the Marshall and Olkin's family of distributions

Abstract

Abstract Marshall and Olkin (1997) introduced an interesting method of adding a parameter to a well-established distribution. However, they did not investigate general mathematical properties of their family of distributions. We provide for this family of distributions general expansions for the density function, explicit expressions for the moments and moments of the order statistics. Several especial models are investigated. We discuss estimation of the model parameters. An application to a real data set is presented for illustrative purposes.

Keywords

• distribuição estendida Marshall-Olkin
• estimação por máxima verossimilhança
• simulação de Monte Carlo
• entropia de Rényi