Abstract Marshall and Olkin (1997)Marshall AW and Olkin I. 1997. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84: 641-652. 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.
Marshall-Olkin extended distribution; maximum likelihood estimation; Monte Carlo simulation; Rényi entropy
